You need to bear in mind that in England, our governments consider us to be total idiots who constantly need to be protected from ourselves. Therefore, all you are likely to find in a bathroom is a light fitting and possibly a shaver outlet which is transformer isolated and limited to 20 watts.

If your bathroom has an airing cupboard with an electric immersion heater (or still has the wiring for one) a 13A socket spurred from that is another option.