I don't know how to find evidence for some of the competences as I don't supervise anyone.  I read recently that I can use examples from outside of work but - while I do participate in activities outside of work - I'm not a "leader".  

Yes, I agree.

Also, I've been a contractor for the last few years, so have done lots of short-term things for organisations who don't want to deal me with ever again.

Furthermore, I'm very modest, and not positive about my skills, even though I'm experienced enough.

I would like to go through the process, but I think someone would have to hold my hand every step of the way.  It's rather daunting.

You do not have to supervise people. You can technically lead people as an alternative. In this way you are responsible for delivery etc but not responsible for day to day HR issues etc. 

I know what you mean.  I am much more of a collaborator and don't like to take the credit for anything - even if it was my idea initially.  It feels like bragging and I'm not comfortable with that.  

I know what you mean.  I am much more of a collaborator and don't like to take the credit for anything - even if it was my idea initially.  It feels like bragging and I'm not comfortable with that.  

Most Engineers I work with say the same. Most find it hard to talk about 'I' rather than 'we'. Few people are really comfortable with it as most of us work in teams.

You will have played your part in that team and your individual actions would have produced great results & outcomes. 

Replace the word bragging with evidencing. You're application is all about what you have personally achieved to reach such a high level of competence. Providing evidence of your achievements is what is required - not something you are choosing to 'brag' about. Be proud of your achievements Karen and remember there is lots of support at the IET should you need it.