Yes, you can fit an electric radiator in a bathroom. You will have to have the electric wire running through to a control box or switch OUTSIDE the bathroom, however.

How much electricity does an Electric Radiator use?
When we ship an electric towel rail, we provide the appropriate sized element to fit the towel rail, to ensure that the rail doesn't overheat, but is sufficient to produce the heat output required to dry and warm your towels.
Click on the towel rail image above to read the instruction manual.
How to fit an electrical radiator element
Although this subject has been covered once already in this blog, I feel it would be beneficial to repeat the advice given:
Make sure that you have the right tools to hand, plenty of space and clean dry area for assembly- Warning: Because of extra danger presented by the presence of water in a bathroom or kitchen the BS approved IE Spur outlet (and towel radiator) must be sited so that it is not possible to touch either when using the basin, shower or bath (refer to BS7671 Wiring Regulations 16th Edition).
The element must be fitted before mounting the towel radiator onto the wall.
Remove 1 transit plugs from the bottom of the towel radiator making sure the rail is upright and sturdy.
Insert the electric heating element (A) into the chosen side of the towel radiator and tighten it into place using a 22mm spanner.
Slide the cover over the element cable and push firmly to secure on bottom of the element.
Follow towel radiator fitting instructions for securing to wall.
Connect the element to the mains power using BS IE Spur socket. If in doubt contact a qualified electrician.
Switch on the socket to heat the towel radiator.- When the operating temperature has been reached, purge excess air from the towel radiator using the air vent.
