You have an earth leakage fault on the socket circuit. That will trip the RCD because that only needs 30mA of leakage to trip it. It won't trip that circuits MCB as that is for a different purpose, overload protection.
It could be any number of things, damp, a pinched cable or several other things.
Make absolutely SURE everything is unplugged. Don't forget things that may be hard wired in like a cooker hood fed from an FCU. Otherwise this is unlikely to be a DIY fix as it is unlikely you will have an insulation tester.