How to recess a recessed socket even deeper into drywall?

I have a standard UK double socket recessed into 15mm drywall. Currently the frame protrudes by approximately 5mm from the wall, and the switches protrude from the frame by a further 5mm.

I wish for the socket to be completely flush with the wall, such that you could run your hand over it and barely know it’s there.

Does anyone know of an alternative faceplate for a UK style double socket which is completely flush with the wall (a bit like the TruFig US one below)?

Alternatively, a good way of recessing my current socket 10mm into 15mm drywall?

This socket will be behind a very, very thin and closely mounted wall mount TV so I don’t mind how it looks, although ideally I don’t want to completely remove the socket.