Hole in wall behind and around plug socket (England, UK) – do I need an electrician to fix?
It sounds like there is no back box on that socket.  Sockets aren't normally screwed directly to walls, but to back boxes that are fitted into the wall.
If there is nothing flammable behind the socket, then that's not actually dangerous.  If there is flammable material, then the socket really should be re-fitted with a back box.
Legally, you can do simple repairs on your own electrics if you are competent to do so.  There is no specific definition of what &quot;competent&quot; is.  I have no way to tell if you are competent to do the work, so the decision is really up to you.