Politically, many come from social conservative backgrounds (Islam is itself socially conservative in many ways), and the first generation of Muslim immigrants in the 1960s/70s, who came predominantly from the former British India, seem to have felt most at home with the Conservative Party, and tended to vote that way - the older generation still does. But in recent elections (particularly 2017) there's been a significant swing to Labour. Neither is the result of the parties 'pandering' to Islam - indeed muslims were scarcely noticed politically until the later 1990s.
Respectfully, I believe you’re being incredibly naive. If you don’t see that the establishment isn’t terrified of being called “racist” or “Islamophobic” and that the police would rather crush those engaging in free speech because it’s easier than arresting those threatening violence due to their “offense”, then I suggest you look a little harder.
How would you know if they’re being “pandered to” or not? There’s cases up and down the country - including all the rape gangs where authorities ignored what they all knew was going on. Their population is doubling each decade and you think they’re “neutral” and politicians don’t notice? Come on.
The followers of Islam do not “out” each other. If someone is a “true Muslim” they believe in Sharia and are anti-individual liberty. They’re also allowed to lie to you to advance Islam. I think the dynamics of what is happening is faster than you’re realizing.