It doesn't always trip power, but I would say there is a 50/50 chance
of it happening every time I use it.

If it is only the washer/dryer that does it, then it is likely to be an
appliance fault. Wiring faults (i.e. neutral-earth shorts) would likely trip
when any high power appliance is used.

I wondered if the fuse in it might not be correct, what fuse
should it be using?

The fuse is irrelevent.

Christian.

P.S. Ensure that you really mean RCD when you say RCD, as many people get
confused as to what each device is called. An RCD is the device on the
consumer unit with the "Press 'T' to test" label on it. It is fairly wide
and probably marked 0.03A or 30mA. The MCBs are the thin ones with the
individual circuits labelled on them and marked with the number of amps
required (i.e. lights are usually B6A, whilst socket circuits are usually
B32A). If it is an MCB that trips rather than the RCD, the problem is VERY
different.

Christian.