Clean it off with bleach then get a dihumidifier like the one I've linked below, that's what I did a few years ago, kept the damp away, it did eventually start to come back about 5 years later but just cleaned it off again before it got bad and has stayed away again, so at worst it should keep the damp away for a few years.
https://www.amazon.co.uk/dp/B007X236NQ/ref=cm_sw_r_cp_apa_fabc_93VMRBTQHWVH0RGZD5RZ
I have a similar problem (also UK), and I'm told the solution is a dehumidifier. I'm currently researching, and this one is coming out top because it can work in the cold (down to 1C) whereas others crap out at anything below 18C.