As The Builder alludes to, this is going to be the RCD that is tripping. It means there is an earth leakage fault, either in one of the appliances plugged into the sockets OR in the wiring of the sockets itself (perhaps induced by the damp, as you mention).
Start by removing ALL devices plugged into the socket system (yes, I mean every one - it is not sufficient that they are just 'off') then try to reset the breaker.
If it fails to reset, the fault is in the cabling to the sockets (perhaps due to damp) and you may need an electrician to investigate further.
If the breaker resets OK, progressively put back the appliances, one at a time, until you find the one that causes the breaker to trip.