I don't live in Copenhagen 🙂 it was my experience regardless of statistics, though. Could just be a month of rain in Manchester before we went home, but who knows. It always just seemed like it had just drizzled a bit.
Iirc this is why Manchester became an industrial city in the first place. It is easier to work with wool when it's humid, and so the spinneries were out in Oldham which is very humid and also in a good spot for collecting the wool from Lancashire. The weaveries were then placed a short distance from there in Manchester, and the cloth was shipped out from Liverpool.
I guess there are a couple of very specific areas that might have less, but overall the country has more rain than Manchester. I do believe Manchester likely gets more rain on those rainy days though. You may have a lot more 'spitters' in Denmark than you do in the UK.
Cotton mostly, not wool, hence Manchester's old nickname of Cottonopolis. Wool tended to go east to Yorkshire, where it was worked in Halifax, Bradford and Leeds. Yorkshire has a lot of sheep, and used to have even more. But otherwise yes, you are correct. The damp climate of North-West England was an important part of it becoming dominant in the 19th century cloth trade, because it made the fibres easier to work with. Cotton fibres are a serious fire risk if they are dry.