Anyone who thinks they are competent can rewire their own home provided they notify LABC first, fill out an installation certificate then have the work inspected (paying the LABC fee of course)
However, it is unlikely that a DIYer will know the regs well enough and will probably not have an insulation tester, RCD tester and ELI tester so they will have nothing of any value to enter into the certificate and then need to call a professional which is then a bit late...
An electrician who can self certify can not certify another persons work unless that other person is directly contracted by the electrician and all wiring is available for inspection. This rule was created to allow the company "qualified supervisor" to inspect and certify work done by the other unregistered (but qualified) electricians working for the same company.
Part P (self certification) has been poorly promoted to the public and the term part P is misrepresented by many including the media. There really is no such thing as "part P" qualified. Part P is simply the document (document P) that that lists the requirements for the electrical part of the building regs.
A much more meaningful term for an electrician who can self certify a domestic installation is a Domestic Installer. There are two types of domestic installer:
1) limited scope (for plumbers/kitchen fiiters etc who need to do their own woiring in connection with their job)
2) Full Scope: Qualified Electricians who do a broad range of domestic electrical work full time.
Many (but not all) full scope domestic installers are also approved contractors working on commercial/industrial applications also.
You can search for domestic installers and see their status on
http://www.competentperson.co.uk/