My original garage floor is dampish through winter, and even three coats of floor paint done in summer over the yers has not solved it completely. But heavy duty carpet tiles contains the dampness. In the new extension side, from 1988, I dug the hole for the pit and lined the whole thing with Visqueen, a clear water barrier membrane. The pit is double thickness concrete blocks, and so far has remained dry, as has the floor, but still covered in carpet tiles. The pit cover is essentially railway sleeper sized timber, but they do swell a bit in winter.
The problem you have with ground water is tricky to sort. Cooperman knows about construction fixes, so might have a solution. Repointing might reduce ingress but the wall of water will still be there. For houses with solid walls, you can drill and pump a chemical into the brickwork to stop damp. It may not stop water but I would think about doing that. We had it done to my Mothers house years ago and it did help a lot.
Also in Summer you could paint the brickwork with anti damp paint. Otherwise stripping the brickwork out and lining the pit is a big job, but would fix it.
