Picture of the double socket, FCU and consumer board. Not sure which circuit it's on, but it trips the switch to left which is down.
Progress
The one which is down, is an RCD. Which means either the live or the neutral, on any one of those circuits to the right of the RCD, has a leak to earth of greater than 30mA. The cause of which, could be absolutely anything fed via that RCD - the wiring buried in the walls, the accessories (sockets, switches, ceiling roses etc.), or anything plugged in. It could even be an accumulation of leakages, of several sources. So likely you can look forward to some fun, tracing the cause...
Your best way forward, is to plug a low wattage table light, or similar, into that double socket, turned on, into which you plug the drier into, and simply work out when the light (and it's socket) goes off - and decide what you were switching on, or off at the same instant it went off.
I think you are suggesting it only trips, when you are using the washer? Is it an older washer? If so, it might be due to carbon dust, from the motor brushes, causing leakage to earth - a fairly quick and easy fix, if that is the cause.