My garage/workshop was just the same - pre-fab concrete construction with a single sloped roof. It's a low ceiling height and it always gets pretty damp in there. And it used to cook in the summer too (dark brown roof!).
We had a new roof fitted professionally, but left the old one in place underneath it. There's about 3" between them, and some insulation. The new roof is made of commercial coil-coated panels, and unlike the original, it's strong enough to walk on, because it's thicker material, with deeper corrugations, and there are strengthening "purlins" underneath it too, on top of the old roof, bearing onto the lightweight steel beams supporting the original structure (which were easily strong enough for all this).
It has stopped "rain" from the inside of the roof completely, but not condensation, because I haven't successfully insulated the concrete slab walls and there is no DPC either.
It's worst in the late autumn and early winter. If we have a run of cold weather, the air dries (Ttrees mentioned this above), and if you then heat it, it can be quite snug, warm and dry (well, not horrid anyway).
We're considering moving house, but if we stay, I may have a go at insulating the walls, which would make a huge difference, but it'll have to be some sort of studwork.
To be honest the best thing would be to carefully dismantle it, keep the roof and rebuild the thing using blocks, on the same or very similar footprint.
It's not a solution for this winter, but if/when you can, I'd strongly recommend putting a second roof over the first one as we did. I didn't have to clear out the garage to do it either
E.
