Range from the cheapest Fit a new plug socket £130 (Certified Circuits based in E16) to the dearest Fit a new plug socket £200 (IH electrical based in E13).
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 E16.

"Fit a new plug socket to a plasterboard wall, on the other side of the wall there's another socket where we can take the cables from"
E3