Have a look at UFH systems, select the one that will do the job, is affordable and will work with whatever your ultimate floor surface will be.
Then look at their specs for thickness of screed above/below and see how much depth you've got to play with once you've added 20mm for your floor plus any depth for fixings
You must get at least 100mm of insulation in and a DPM. If that clay is as firm as it looks you could probably skip hardcore so go sand, dpm, insulation, concrete, ufh, screed.
Usual thicknesses (in the Approved Docs, well worth a read) are hardcore 100mm, sand 50mm, insulation at least 100mm.
You may/may not be aware but this is notifiable work (renewing thermal elements, structure), if you're planning on DIYing it (and the rest of the floors) then download, read and comprehend the approved docs then put a Building Notice in. Building Control are not there to tell you how to do the job, they are there to ensure its done right. BUT if you do your homework & go to them with your scheme (along the lines of 'here's what the ADs suggest but I don't have the depth. Can I do this instead') then you may get lucky