Assuming the washing machine is in the kitchen, then, the answer is yes, but as a 'special location' (as defined in part p of the building regs) then the works will need to be undertaken by a 'competent person'

The switch above the worktop will more than likely be supplied from the ring circuit supplying the room, if this is the case the least disruptive method would be to install a dual 1 gang surface pattress over the top of the existing backbox (assuming its flush mounted behind the tiles), refitting the connection unit (switch) in one half of the box with a single socket outlet in the other.
The box will sit proud of the wall by 35-40mm so will stand-out if all of the other accessories in the room are flush mounted.

If you are patient and have a small angle-grinder you could replace the existing flush backbox with a dual flush backbox.

Posting a picture of the existing arrangement might help with other ideas.

Paul

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Dual surface back box:


Dual flush back box: