Should I be presented with a electrical certificate by law after a full rewire?

Yes. EIC cert required and the job notified to Building Control.

Yes, any type of electrical work you have had carried out at your property, you should have been issued with An Electrical Installation certificate, failing that if it was a small job, then a minor works certificate should have been presented.

Without doubt, not only should you be presented with a full electrical installation certificate (EIC) on completion of works and test & Inspection, you should also be presented with a copy of the 'Building notification' certificate, this notifies the local authorities that these notifiable works have been undertaken by a registered, competent and qualified installer.

Yes, EIC (Electrical installation certificate) should be issued.

Certificates call for those responsible for the electrical installation or construction work to certify that the requirements of the Regulations (BS7671) have been met.

Yes , every electrical work carried on the property should come with an EIC certificate

For a rewire you should expect an EIC - Electrical Installation Certificate, if you had smoke / heat detectors installed (even if they were long life battery ones) you should be given a BS 5839 Pt6 smoke detector certificate. In England / Wales the job requires building control notification paperwork, this is not the case in Scotland (even though the building standards are much tighter here)