Sorry for the late response but been on nights. Thanks for all the input, I'll try and answer all your questions.
Out of habit we've never used both appliances at once as 'something' used to trip. Its been years since it last happened and I couldn't remember if it was the RCD(63A/30mA trip), fuse in the extension, fuse in the appliance plug or fuse (15A) blowing in the ancient consumer unit.
So I spent ages yesterday playing around and watching the appliances run but couldn't for the life of me get anything to trip
The only thing noticeable was the extension lead plug getting hot.
The only difference between now and 5 years ago is a new washing machine. Does it have a different power consumption? did the old machine have an electrical fault? No idea! So I'm no wiser as to what the old problem was but I don't remember the hassle of finding and replacing fuses or fuse wire etc which makes me think it was the RCD that used to trip, so probably the old machine was faulty. If my girlfriend could sort it I'm sure it'll have been the RCD switch!
When I run 1 machine at a time, things are absolutely fine- no overheating of plugs or blown fuses etc. Running them both at the same time on different sockets or different circuits, again is fine.
As most of you have said, my current set up is probably dangerous if I use both apps at once so would still like to change the sockets.
Changing to 2 sockets is a good suggestion but I'm limited by wall space so the socket would have to go behind the appliance.
The reason i wanted to change them to FCUs was to save having to slide them out if there's a problem and knackering the flooring plus its easy to turn them off when we go away. The flex on the appliance is too short to put the socket where its easily mountable and I want to stay away from joints or extensions.
So given that my trip problem seems to have gone away, will my original idea of 2 FCUs be okay?