Since a person without a CEng can be a notary public, I'm sure it's possible for a CEng to be a notary public too.

But I can't see any way that a CEng helps you towards becoming one.

https://www.thenotariessociety.org.uk/pages/becoming-a-notary

Why?  Qualification for CEng has nothing to do with the qualifications required to be a notary public.

The qualifications for becoming a notary public are listed at 

https://www.thenotariessociety.org.uk/pages/becoming-a-notary

Synopsis: you need a law degree, or are already a solicitor or barrister.

Philip Wardle: 
Agreed Simon - although as many will be aware, in the UK an 'engineer with professional qualifications' is accepted as ‘a person of good standing in their community’ for the purpose of countersigning passport applications and photographs - https://www.gov.uk/countersigning-passport-applications  I believe anyone registered with the Engineering Council would easily qualify - CEng, IEng, EngTech or ICTTech.

Also includes the following:

• member, associate or fellow of a professional body

I agree with Simon Baker, any one who is a professional in UK and has had a good charater without any conviction can authenticate documnets. I have authenticated documents for Passport, Visa and Naturalisation applications. The UK Border Agency has never complained about it.

I doubt that Simon said or meant that “authenticating documents” can be accomplished by people like us. Amongst other things, because it is not true, which is why there are notaries. 

People leave their wills with lawyers, rather than with the next door neighbours or relatives (imagine the fun if five or six supposed “wills” turn up in the hands of different relatives, all nominally “authenticated” by “persons of good standing”). Trained and registered agents, not “persons of good standing”, intermediate the selling of houses. 

There are indeed a limited number of cases in which a simple statement by “persons of good standing” is legally required and has effect. In previous years, affirming a likeness of a person known to you on a photograph accompanying a passport application was one. 

Credit cards (Visa, Mastercard) are a private matter; companies can do what they like. For some things they will engage a notary.