I have the exact same problem! Although my cellar has a brick floor and there has been flooding before. It's been a massive job...

Firstly the walls were covered in some impermeable paint which was allowing moisture to build up behind it, causing condensation on the walls. I have spent several weekends removing the paint, and the room has dried out considerably. Next job (still ongoing) is lime washing the walls, done a few coats this helps the masonry breathe properly it takes 4+ coats for a decent finish.

Also before getting to the brick floor it was originally covered in 3-4 inches of mud / wood which had disintegrated which needed digging out... I've scraped out between individual bricks and will be brushing mortar between them over the weekend. When I inherited the cellar all the vents were blocked so It is still drying out in places. I may need to add a pump at some point in the future, in case of flooding.

There is a problem with condensation although any tools hung up are fine, just anything on the floor when picked up has water droplets on it.

So I can recommend lime washing your walls!