I don’t know if this helps?

https://www.homebuilding.co.uk/advice/renovating-old-floors

Thank you for the link

What kind of flooring are you hoping to get installed?

The builders who recommend to screed over the quarry tiles, what kind of flooring do they recommend putting on top of the concrete? Is that going to make the floor less cold? Without a DPC, isn't there going to be a risk of efflorescence? You'll still have to deal with vapour coming up through the floor, so you'll be limited in the kind of flooring you can use. I doubt you could put vinyl flooring without a vapour barrier, but I'm not sure.

I'm not an expert, but (assuming your floor is original) unless you insulate the floor, it will continue to be cold. And to insulate the floor, you will have to dig it out unless you have enough head room to raise it. You could potentially install a wooden floor so it doesn't feel as cold, but it would need breathing room underneath to avoid damage from the ground moisture. You could also add vapour-permeable insulation underneath.

As for DPC causing damp walls, what do the builders recommending it say about that? My understanding is that you could put a drainage system on the inside of the house, under the slab, (example: https://hammerandhand.com/best-practices/manual/7-basements/7-4-basement-retrofit/). It might still be a good idea to insulate the floor to avoid condensation issues.

I would personally consider a proper DPC to decrease the humidity inside the house, especially in a humid climate, but it's an expensive intervention. As water turns into vapour, it uses up energy (heat) and cools down the air. Without a DPC, the more you heat your place, the more water from the ground turns into vapour and gets into your house, so it's not very energy efficient.