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Sockets can fail like that. I've replaced 2 recently. It's not really worth diagnosing, just change it for another one.
If you have a torch and no multimeter (should really be a voltage tester) the easiest approach is switch off all the power at the consumer unit and replace it.
As has already been mentioned, it's possible internal corrosion is playing a part.
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That does look like a 'damp zone'.
Maybe consider one of these as a replacement:
https://www.toolstation.com/bg-ip66-13a-switched-socket/p78539
The right hand side of this dual socket has stopped working. Loose wire? Something else?
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