IMO a culture is not just a set of protocols or rules written down by some chronist/sociologist. To me culture is more about how people live in a certain place, their routines, their customs.
Again, I'm not particularly talking about Muslim population, but since you continue with them, I will do the same :) (I guess it's an easy example since they are really a big community all around EU)
Now take any East London borough with a high % of Muslim. If you compare it with how it was let's say in the 80's you will probably see several differences in: the language most people talk to each other in, the way kids are educated at home, the way people interact with their local store owners, the food people eat, dress codes, etc.
If a person from a distant remote place visits that same borough in the 80's and today he will see two culturally different places. That's because the inhabitants of the place, make the culture. That's my view!
This reply is just intended to challenge your view that big numbers of immigrants has no influence on the culture of a country/city/place/population. I'm not implying that borough was better in the 80's than now!
>>Mosques are very underrepresented, considering the number of muslim, and they have to fight for every single one.
I really don't know where you draw the "fair representation" line. E.g. Greater London has 650k Muslims, and around 411 mosques. That's roughly 1400 Muslims/mosque. What would be a fair representation in your opinion? In contrast there are 450k Hindus in Greater London, and I couldn't find the number of temples in any source, but I'd guess it's around a few tens. Maybe this is an unfair comparison since a temple is much more of a requirement for Muslims than for Hindus, I really don't know that.
>> They don't make anyone else follow their rules, in any case.
They raise their kids with "their" rules, which is not even theirs, it's basically dictated by some kind of dogma. These kids will be the future generation of that place.