Nothing wrong with your solution, though it depends on having sufficient
ways in the CU and is only really achievable in a rewire. When you say
this
is the correct solution, how is it more correct than the OP wiring his
appliances into the ring (which is what I would do using FCU's as they are
fixed appliances)

The current wiring regulations require you to consider the ring balance. In
particular, it is not permitted to "design in" substantial and foreseeable
point loads. Personally, I think running all the laundry off one double
socket is a substantial and foreseeable point load and is poor practice when
designing the circuits. That is not to say that an existing system should be
regarded as dangerous or requiring rectification, it is just good practice
when designing a modern installation.

Christian.