Sockets don't have a maximum power rating, per se. (Well, not different to the maximum 13A load that they're designed for, anyway). So it must be the cabling to the socket that has a restricted power load. Therefore anyone seeking to upgrade the socket's capacity would actually have to change the wiring that feeds it.
Your 'electrician' (if he really was one, as he doesn't seem to have been following the law on electrical installations in any way at all) probably tapped into a lighting circuit, rather than one designed for supplying power to 13A sockets, which would explain why he needed to caution you about the maximum load you could use the socket for.
To upgrade the socket to do its job properly, a (qualified!) electrician would need to investigate whether it was possible to add it as an extra socket on an existing ring main or to take it as a spur off one. Any difficulties involved would largely depend upon how easy or difficult it would be for him/her to access the ring main from the socket's location. (The 'electrician' who fitted the socket in the first place clearly didn't think that it would be an easy task!).
This picture might help to explain things:
https://i.postimg.cc/jjjfHtGW/Sockets.jpg
The person upgrading the socket would need to either wire it in as part of an existing ring main or to run it as a spur from a socket on the ring (but not from a socket which is itself a spur). That would be quite likely to involve lifting floorboards and/or accessing a ceiling void and/or chasing a cable into a wall in order to do the job properly. (It all depends upon where your existing ring main wiring goes and how easy it would be to connect it up to the socket).