There are a number of aspects of your question that are puzzling. 


Firstly,  and directly relevant to your first question is the fact that your degree is accredited by other Institutions but not IET. 

The delegation by Engineering Council for accreditation is, sensibly,  on a sectorial basis, - in other words,  the qualification has to be relevant and sufficiently rigorous to demonstrate knowledge & understanding relevant to the domain covered by the engineering institution involved. To be absolutely clear,  it is no more nor less than that - a means of demonstrating k&u. To illustrate with an extreme example,  would you expect the requirements of k&u for an electrical engineer to be met by a M.Eng in Civil Engineering?


So,  to state what may appear obvious,  a degree in Mechanical Engineering may have no relevance to an application associated with Electrical Engineering and vice versa. 

You don't tell us what your M.Eng is, but if it's accredited by I Mech E, but not IET, this suggests it has more relevance to mechanical engineering than to electrical engineering or other related disciplines covered by the IET. 

So, depending on  what that degree is,  the simple answer may be that, yes,  you have chosen the wrong Institution if your area of practice is more aligned to those of a different Institution (e.g. I Mech E) than to IET. 


However,  as your employer has pointed you in the direction of the IET, I can only assume that your area of practice is more aligned with that of the IET. 


So, the acid question is whether your employer's guidance was correct or not  - are you practising in an area not covered by the IET, e.g. mechanical engineering, or are you practicing in an area covered by the IET?

if you're not practicing in an area covered by the IET,  then the simple answer is that your employer's guidance was wrong,  you have joined the wrong institution. If not,  then I suggest the important question is how relevant your degree is to your area of practice.  The accreditation of qualifications is much more than a tick in box exercise.  If it does not demonstrate knowledge and understanding relevant to your area of practice and that for which you are seeking C.Eng accreditation then you will have to provide evidence of knowledge & understanding in other ways.  That means that you have to make the choice - pursue C.Eng via an Institution that accredits your degree but which may appear irrelevant to your area of practice (though if you're not practicing in that body's area of relevance,  you are likely to fail) or provide evidence of knowledge and understanding relevant to practice in an area relevant to the IET in an alternative way than the exemplifying qualification. 


The good news is that the exemplifying qualification is not the only means of evidencing relevant knowledge and understanding.  Knowledge and understanding may be evidenced by diverse means without reference to how that k&u has been attained.

For instance,  I have known people who attained their degree in a wholly unrelated subject but have then diversified to practice in a wholly unrelated area (in sine cases not even an engineering degree) and have gained their k&u by on- the- job learning.  That is completely acceptable providing it can be evidenced.  Possession of an accredited qualification only brings the benefit of not having to provide further evidence of k&u.


So, this brings me to my second area of puzzlement  - when you mention other institutions that accredit your degree,  you mention IEE - the IEE has not existed for more than 20 years.  The IEE merged with other institutions (e.g. the IIE) to become the IET. This makes me wonder about the currency or efficacy of your information on which institutions accredit your degree. 


This brings me to what I consider the most important aspect of your questions,  your second question.  The exemplifying qualification is no more than a means of evidencing k&u. C.Eng is massively more than k&u. If it weren't,  what value would it offer? K&u is no more than a starting point,  a baseline. Hence there is no way that the exemplifying qualification is going to be sufficient alone. The answer to your second question is neither of those options.  The possession of an exemplifying qualification does not exempt you from the need to evidence how you meet the other competence categories in UKSPEC.


We need to know how you apply your engineering knowledge to your engineering practice


As UkSpec makes very clear, among other factors,  to attain C. Eng,  you have to provide evidence that you hold the theoretical knowledge to solve problems in new technologies and, very importantly that,  in your engineering practice you successfully apply that knowledge to deliver innovative products and services and/ or take technical responsibility for complex engineering systems. Additionally, you have to demonstrate that you carry accountability for project,  finance and personnel management,  including managing trade- offs between technical and socio- economic factors,  that you hold the skill sets necessary to develop other technical staff,  provide effective interpersonal skills in communicating technical matters,  that you deal effectively and consistently with matters of safety and sustainability and that you do all of the above ethically. Little of this will be demonstrated only by holding a M.Eng degree, whether accredited or not. 


The IET offers Professional Registration Advisors (PRAs), volunteers who help you understand the requirements and prepare your application.  Based on your question,  I would suggest you are in strong need of this guidance,  so would urge you to request that you be allocated a PRA if you intend to pursue registration. As a registration interviewer,  I find that candidates who do not avail themselves of that opportunity often have difficulty demonstrating that they meet the requirements.


C. Eng is the Gold Standard for engineering professionalism with International acceptance, not a tick in box exercise. You are already entitled to use the designatory initials of M.Eng and MIET, to add C.Eng requires a much stronger demonstration of practicing professionalism and if it didn't,  it would hold no value. 

There are a number of aspects of your question that are puzzling. 


Firstly,  and directly relevant to your first question is the fact that your degree is accredited by other Institutions but not IET. 

The delegation by Engineering Council for accreditation is, sensibly,  on a sectorial basis, - in other words,  the qualification has to be relevant and sufficiently rigorous to demonstrate knowledge & understanding relevant to the domain covered by the engineering institution involved. To be absolutely clear,  it is no more nor less than that - a means of demonstrating k&u. To illustrate with an extreme example,  would you expect the requirements of k&u for an electrical engineer to be met by a M.Eng in Civil Engineering?


So,  to state what may appear obvious,  a degree in Mechanical Engineering may have no relevance to an application associated with Electrical Engineering and vice versa. 

You don't tell us what your M.Eng is, but if it's accredited by I Mech E, but not IET, this suggests it has more relevance to mechanical engineering than to electrical engineering or other related disciplines covered by the IET. 

So, depending on  what that degree is,  the simple answer may be that, yes,  you have chosen the wrong Institution if your area of practice is more aligned to those of a different Institution (e.g. I Mech E) than to IET. 


However,  as your employer has pointed you in the direction of the IET, I can only assume that your area of practice is more aligned with that of the IET. 


So, the acid question is whether your employer's guidance was correct or not  - are you practising in an area not covered by the IET, e.g. mechanical engineering, or are you practicing in an area covered by the IET?

if you're not practicing in an area covered by the IET,  then the simple answer is that your employer's guidance was wrong,  you have joined the wrong institution. If not,  then I suggest the important question is how relevant your degree is to your area of practice.  The accreditation of qualifications is much more than a tick in box exercise.  If it does not demonstrate knowledge and understanding relevant to your area of practice and that for which you are seeking C.Eng accreditation then you will have to provide evidence of knowledge & understanding in other ways.  That means that you have to make the choice - pursue C.Eng via an Institution that accredits your degree but which may appear irrelevant to your area of practice (though if you're not practicing in that body's area of relevance,  you are likely to fail) or provide evidence of knowledge and understanding relevant to practice in an area relevant to the IET in an alternative way than the exemplifying qualification. 


The good news is that the exemplifying qualification is not the only means of evidencing relevant knowledge and understanding.  Knowledge and understanding may be evidenced by diverse means without reference to how that k&u has been attained.

For instance,  I have known people who attained their degree in a wholly unrelated subject but have then diversified to practice in a wholly unrelated area (in sine cases not even an engineering degree) and have gained their k&u by on- the- job learning.  That is completely acceptable providing it can be evidenced.  Possession of an accredited qualification only brings the benefit of not having to provide further evidence of k&u.


So, this brings me to my second area of puzzlement  - when you mention other institutions that accredit your degree,  you mention IEE - the IEE has not existed for more than 20 years.  The IEE merged with other institutions (e.g. the IIE) to become the IET. This makes me wonder about the currency or efficacy of your information on which institutions accredit your degree. 


This brings me to what I consider the most important aspect of your questions,  your second question.  The exemplifying qualification is no more than a means of evidencing k&u. C.Eng is massively more than k&u. If it weren't,  what value would it offer? K&u is no more than a starting point,  a baseline. Hence there is no way that the exemplifying qualification is going to be sufficient alone. The answer to your second question is neither of those options.  The possession of an exemplifying qualification does not exempt you from the need to evidence how you meet the other competence categories in UKSPEC.


We need to know how you apply your engineering knowledge to your engineering practice


As UkSpec makes very clear, among other factors,  to attain C. Eng,  you have to provide evidence that you hold the theoretical knowledge to solve problems in new technologies and, very importantly that,  in your engineering practice you successfully apply that knowledge to deliver innovative products and services and/ or take technical responsibility for complex engineering systems. Additionally, you have to demonstrate that you carry accountability for project,  finance and personnel management,  including managing trade- offs between technical and socio- economic factors,  that you hold the skill sets necessary to develop other technical staff,  provide effective interpersonal skills in communicating technical matters,  that you deal effectively and consistently with matters of safety and sustainability and that you do all of the above ethically. Little of this will be demonstrated only by holding a M.Eng degree, whether accredited or not. 


The IET offers Professional Registration Advisors (PRAs), volunteers who help you understand the requirements and prepare your application.  Based on your question,  I would suggest you are in strong need of this guidance,  so would urge you to request that you be allocated a PRA if you intend to pursue registration. As a registration interviewer,  I find that candidates who do not avail themselves of that opportunity often have difficulty demonstrating that they meet the requirements.


C. Eng is the Gold Standard for engineering professionalism with International acceptance, not a tick in box exercise. You are already entitled to use the designatory initials of M.Eng and MIET, to add C.Eng requires a much stronger demonstration of practicing professionalism and if it didn't,  it would hold no value.