This is a damp cellar. That is something good. It does not damage houses. It is just not made for metal tools. In ours, I once tried storing apples as long as they would last, which was 3 winters, though old varieties.
If you really can't resist, you have to do the joints besides the floor: scrape out and put in plastic-reinforced joint mortar. You can do that, convert such a room. I had a neighbor who did that, it stayed nice, it went like this: a floor slab, then screed and tiles, all floating. The floor slab was about as thick as for a garden shed. But the story doesn't end there, it will remain damp for a long time, dryers will be brought in down there, later a small fan heater will move in, it’s dark too and there will quickly be blemishes on the wall if painted. For a damp cellar being stubborn is expensive but if it's worth it to someone?
On terribly hot days, I have had cellar dinners down there, long table, white linen, candlestick, staying until one gets chilly. Wonderful!
Many greetings
Gabriele