You need to find out.I don't know the situation with regards to building control
Apart from the difficulties of finding an electrician to falsify documents to say that he did the work (and frankly you should run a mile from anybody that dishonest anyway), there's the risk that that might not be what BC are expecting.
For all you know the original application said that a 3rd-party certification would be done, so an electrician popping up saying "it's all me own work, guv" is going to ring alarm bells.
Ditto if the plan was DIY electrical work and a satisfactory inspection and testing by an electrician. Which incidentally would be the ideal situation for you, as that would be easy and non-contentious to arrange.
You should ask them what the original application was based on, and what outstanding actions are needed to ensure that the project remains on track and completes successfully and in a way with which they are happy.Building Control have apparently signed off the renovation and are just wating on the electrics to be finished before they're happy.