Apart from the financial aspects of getting the appropriate equipment, it is not difficult to become competent to test your own installation work to confirm that it's OK.
General I&T competence needed to certify other people's work, carry out PIRs and fault finding etc is indeed a very different kettle of fish, but he doesn't need that level of competence.
I have a 17th Edition C&G Certificate (Installation, not Testing)
Which one, exactly?
Basically if you want to stay within the law then you need to find out what your council will accept. It may be that your qualification will be enough, but you still have to notify in advance - the best you can hope for is that they will charge you a lower fee.
It may be that they don't care, and will charge you the full whack, and will come along and do their checks and issue the completion certificate.
It may be that they don't care, and will charge you the full whack, and then insist that you arrange and pay for an electrician to inspect and test. They aren't allowed to do that, of course, or to make you pay extra for them to sub it out, but many councils try. If all you are doing, Building Control-wise, is a rewire, and you don't have other reasons for wanting to not upset them, then you need to decide how far you are prepared to push back against their behaviour.
As far as EICs go, there are no formal restrictions on who can issue those, and as an engineer you can (presumably) be trusted to know whether you would be justified in signing the declaration on one.