Plug socket won't turn off even after replacing
It must be a coincidence, I'd take the faulty socket back to Screwfix and get a replacement.

After removing the socket and disconnecting it from any wiring, you could test the switch with a continuity tester.

The only alternative explanations would be quite complicated. Even an overload is unlikely to produce the exact same symptoms in a new and a 20-year old socket. Anything that welds contacts together ought to trip a breaker, make a noise, a smell and leave visible evidence.