My sister told me how lovely her friends house was with underfloor heating, and I had stopped in a boarding house with a black tiled floor outside the shower within the shower room and yes it was lovely stepping out onto a lovely warm floor, which dried quickly.
When fitted to mothers wet room we made errors. One was sculptured tiles, fitted for extra grip, but do not drain as well as smooth so stay wet. The other was the pocket holding the sensor had too sharp a bend, so when the sensor went wrong we could not renew it.
The first job was a band jack and remove the original floor, then polystyrene blocks fitted covered with around 15 mm thick plywood to stop heat going down into the floor, the polystyrene blocks around 4 inches thick. The heating cable was then laid and a special glue used to fix the tiles on top, this caused a problem first time around as out of date and would not set. A towel rail was also fitted.
The room is around 1.5 meters x 3 meters and the heating cables span whole floor, toilet is held on wall so even under toilet is heated. The tiles are slow to heat, takes around 1.5 hours for them to reach temperature, and the shower soon cools them, so after a shower it takes around 1/2 hour to dry floor if surface water is swept to drain. However if towel rail is turned off, then around the coldest room in the house. Other than warm feet it seems to make no effect to general heat of the room. In all very disappointing.
So I looked at the maths, the towel rail is at around 70°C that's 50°C over the temperature required for room, and around 1 meter² surface area, the heat output is not linear the curve goes up as temperature increases, however for simplicity late us say it is. So floor is 4.5 meter² but just 7°C differential. So 7 x 4.5 = 30.5 and 50 x 1 = 50 so at least 40% extra heat, by time you add the fact it is not a straight line graph and it does not auto start an air flow, one is looking at the towel rail being over twice as good as under floor heating.
Underfloor heating "Hypocaust" has been going for a long time
picture of some early examples, however we have learnt it simply does not work, we stopped using underfloor heating for some 1500 years, there is a reason, it doesn't work. Yes my son have underfloor heating, and yes it does what he wants, that is to cool the water in the Aga back boiler when it is too hot, it is a method to store heat, so the bedroom floor gets warm and the standard central heating radiators turn off. But the energy is stored in the floor, so heating would need to be on 24/7.
Today we are looking at the reverse, swapping standard radiators for fan assisted radiators so rooms warm up, and of course also cool down quicker than with standard radiators. This means less time is required to heat the house so heating can be automatically turned on with geofencing as it detects our mobile phone getting close to home. Not saying it works, it is still too slow heating the house. But we are dumping storage radiators and going for speed heating the home, and you are trying to return to Roman times, still trying to live in the 1st century not the 21st century.