I agree with buildersmate regarding the fact that it would be questionable that the u/f heating would trip anything out by demand alone. If however it had a fault on it, possibly intermittent then that would cause a problem. I have installed a couple of systems but these have always been on a mat and a metre square was not available, at that time, as far as I can recall these have to be on a seperate supply to anything else and don't forget that a bathroom is classed as a special location by the IEE, so anybody working on electrical equipment within that area must hold a part P certificate. It's been a long time since I done My 16th edition, but I know that the part P thing is still compulsory. Towel rail, yes I had one In a bathroom 8 ft square and that did provide a good heat source and dried the towels provided you don't have the window open all day. I would be inclined to ask to see his certification before going any further.