Range from the cheapest Fit a new plug socket £120 (Gsi-Gas based in SE5) to the dearest Fit a new plug socket £200 (Matrix Electrics based in SE21).
Comparing electricians estimates for a Fit a new plug socket gives you an idea of who will be better value but the best way to compare costs is to get actual quotes.
What to do - Get rates and quotes by posting your job to fit a plug socket to electricians in SE22.