Was going to say similar to BlodPlod
You can get low profile UFH systems which sit on top of your existing floor, so you don't have to dig it up. They raise your floor level by only 18mm (you can get even shallower systems at 15mm). Quite a few manufacturers do them, not just Polypipe. Nuheat do one, for example.
One of the handy things about the low profile systems is they work more like radiators because the pipes are close to the surface, so they are more responsive; heating up and cooling down quicker. They are not quite as efficient as the other type of UFH where the pipes are buried in the screed which acts as a thermal store and you generally keep it on a low temperature all the time, programmed to warm up at times such as in the evening.
I found the underfloor heating store very helpful with advice:
www.theunderfloorheatingstore.com/prowarm-low-profile-kits
I have their system (as above), which is ProWarm. I haven't moved in yet (plus, it's summer), so I can't tell you what it's like to live with.
It wasn't that expensive to install. I could have saved money with bog-standard radiators, but if I had wanted designer radiators, I probably wouldn't have saved much.
I had great difficulty with finding someone willing to quote to fit it, however. Fortunately, the builder I chose has a working relationship with a young'ish plumber who is used to fitting UFH. He hadn't done the low profile stuff before, but was happy to do it. I think he gave me a good price.
I would ask your builders if they know any plumber who do UFH. In my experience, if your builders don't want to do something, you might be better off finding a specialist to do it instead.
I'm so excited to try my underfloor heating (without wishing away the summer of course
)