A couple of comments, then some suggestions.
It might help to explain that there are 2 types - water-based pipes that run in the floor and electrical matting. You are wanting the latter type.
It won't be relatively cheap to run if you are operating it on expensive peak-rate electricity.
Next the insulation under the floor. If your house is newer then 4 years old then you will have a higher standard of insulation under the floor. This prevents your expensive heat being conducted downwards and lost into the subsoil below your house (never wondered why the creepy-crawlies enjoy finding places to overwinter snuggled up close to the outside walls of a house?). This is going to be a particular issue for you if you have a solid concrete slab screed on the ground floor – less of an issue if you have wooden floors on the ground floors (as older houses did). The very fact that you are heating the floor makes this important. It is not an issue for the answer given above because in the first floor bathroom the floors are wooden anyway. Yes, do use these insulation boards your OH has found but see the clearance issue below. To give you some idea, my house has 100mm thick insulation board to stop me losing much heat downwards - you won't be able to achieve this much because of the height issue but do put in what you can.