The RCD tripping when using your washing machine could indicate that the electrical insulation/motor or other electrical component is breaking down causing the trip. It could be considered an early indication that your washing machine is failing. It could also mean your washing machine could be leaking and water tracking is causing enough earth leakage to trip the RCD. You could have your washing machine PAT tested to rule out a faultly washing machine.
As Adam suggests is the socket that the washing machine successfully works on also protected by the RCD. If the RCD is tripping then its not a load issue. If its the fuse or mcb then it is a load issue.
Matt
January 2009