In order to comply with the 300+ pages of British Standard 7671, also know as the Wiring Regulations, you must issue a certificate, as prescribed in Part 7.
Only those responsible for the Design, Construction and Inspection & Testing may sign to certify compliance. In order to do this you must be competent, which is defined in the Electricity at Work Regulations 1989:
"No person shall be engaged in any work activity where technical knowledge or experience is necessary to prevent danger, or where appropriate, injury, unless he possesses such knowledge or experience, or is under such degree of supervision as maybe appropriate having regard to the nature of the work."
A suitably qualifed electrician could, indeed, act in a supervisory capacity and sign for work carried out by you to his satisfaction. The certificate then states that the installation complies to BS 7671 and the 'guilty' parties are identified.
However,
the law now requires that electrical work in domestic properties also complies with all relevant building regulations, for which you need to submit a building notice if doing it yourself. A building inspector, depending on which local authority you come under,
may then accept your BS 7671 certificate as evidence, but local authorities have a degree of autonomy in how they enforce the building regulations. You would have to check with them.
The other option is to use an electrican registered with a self-certification scheme, who can do the work, issue the BS7671 cert and then retrospectively notify the local authority. In doing this he is not just notifying compliance with BS 7671, he is stating that his work complies with all relevant building regulations. He cannot, however, do this on behalf of
your work, because the rules of his registration do not allow it, no matter which registration body he belongs to.
If you've already done the work (sounds like you have) you should contact the local authority building control office and ask them what you need to do. They may accept (on payment of a building control fee) a Periodic Inspection Report by a competent electrician... which is the only legitimate way to get retrospective certification that an installation complies with BS 7671.
You will need to show building regulations compliance should you come to sell the property.