It's a bit more than just a "bend" in some respects
Incidents such as the Woolwich attack are an extreme manifestation of the frustraghtions that exist throughout much of the Muslim community. Yes, a tiny minority would contemplate/support such an attack, but significantly more support the sentiment behind it.
Many of the difference's aren't purely cultural. They've been enshrined in law/policy and would require a chnage in law/policy if diffrences are to be reconciled. Religious law for example, isn't widley know for it's flexibility.
Foreign policy is a large sticking point. So is freedom of expression, be that religious, political or sexual etc. Equality for all is also at odds with what you call Muslim "culture" but in reality is Islamic law. These views aren't nesisarily "extreme", but it's very hard to see how they're compatible with the majority of UK public opinion. I just can't see a satisfactory compromise.
There's only one way you can resolve conflict without bloodshed, that's at the ballot box. The issue for Muslims is, they're a minory comunity with a strong cultural identity but will always been out voted on policy issues. The electoral system dosen't offer a voice for minority views so the more moderate message gets compleatly ignored.
Then there's the extreme views which are held by a small but significant number, which are clearly intolerable but continue to be shouted very loudly by supporters, and creates more resentment from all.