If you are saying that 1 x single fused spur (rated max 13a) is the source for both the washing machine and dishwasher power, then thats wrong.
On heat / boil water demands with both appliances running I think you will pop the fuse frequently.
They need seperate fused spurs, and a spur off a spur isn't going to do the job. You will need to take from another socket on the ring circuit.
Unless, the existing spur is actually part of the ring which can be investigated- the big clue would be 2 x twin / earth cables terminated as ring in / out in the existing spur.
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