13A socket in bathroom?

[clockworks]

I live in a 4 bed dormer bungalow. I use the upstairs 2 bedrooms as a workshop and a storeroom for my small business, and the shower room for cleaning parts. I have an ultrasonic cleaning tank set up on a trolley next to the basin, and I plug it in using an extension lead that runs off to one of the bedrooms.

The extension lead is a bit of a trip hazard, and I can't shut the doors while it is plugged in.
Can I legally fit a 13A socket in the shower room?

[clockworks]

Thanks for the replies.
I have a modern board. The previous owner had it replaced, so less than 8 years ago.
Socket would be 2m from the edge of the shower tray.
Power consumption of the ultrasonic tank is 540W.
I would be fitting the socket myself, onto it's own breaker in the CU.
If I sold the house, or started using the shower room for it's intended purpose, I would remove the socket and fit a blanking plate.