Look up micro bore systems - I don't have experience of them but the architect and builder here seem fairly confident. We have a room which will span a concrete base (don't want to dig deep) and a new base which we can put ufh on without issue.
Whether or not the extension would be freezing would depend on a range of factors, such as, what is the external wall construction, what provision of insulation do you have in the walls/ceiling/floor, what total area of glazing do you have, what the height of the room is etc. Also do the two radiators of sufficient size/design to provide the correct Watts/BTU's required to heat the room?
I have just designed an extension for a client to replace an existing conservatory (although the extension was slightly larger than the existing extension) and they were worried about the heating within the room as they had a vast area of glazing to the walls (think sunroom / bringing the garden into the room idea) and they also had 4 veluxs within a vaulted ceiling. We are in Scoltand just for the record! I have put two double convector heaters of appropriate size within the extension and they are so pleased that the room is now usable (previously unable to utilize the extension in the winter/height of the summer). They have actually commented that the extension is warmer than their livingroom considering the vaulted ceiling and vast area of glazing!
You can get high level radiators (only problem is heat rises) also or electric radiators that go 'under your kitchen units' int he plinth. Could your architect not review your plans with you and point out any amendments that could be made to allow for a radiator to be positioned in/adjacent to the kitchen?
I am personally not a fan of underfloor heating though choice is solely yours. With the correct insulation and correct radiator sizes your extension should be toasty warm.
Sorry to post and run. Thank you so much for your replies. I'm feeling a little more relieved and am off to investigate your suggestions. I need to make a quick decision as I'll be holding up the build if I diliberate for too long.