Hi, yes what you suggest is fine. My mothers house which was built in 1999 has exactly what you have the only difference is she has 20a DP switches instead of FCU's. When she moved out of the house we discovered that the DW and WM where plugged into the single socket with a 4 way extension lead under the plinth ! It worked for years with no problems.
If you washing machine has a hot water intake that's even less likely to be on a boil wash !
My original suggestion was a 32a switch which will give you plenty of connection space and a good quality one has 2 sets of screw terminals.
I stay clear of the cheaper Con-verta sockets and buy a 1gang to 2 gang conversion box and use an MK or Crabtree socket.
This is a tile save solution. The only other option is an additional socket supplied from below
Regards,
DS
Presumably the solution we are now discussing must rely on each appliance therefore having a 13A fused plug, particularly as we are getting rid of the FCU? Would you mind linking me to your recommended switch and socket please so I know I'm getting the right thing?
I see you can also get DP FCUs - would I be right in saying that the only difference between that and a DP switch is the fuse, otherwise they are doing exactly the same job?
My washing machine does not have a hot water feed by the way...