Yes, for decades now they've been spouting off about secular humanism, or about their status as a "post-Christian" nation (which is pretty screwed up all by itself, given the origin and continuing structure of the Church of England). I'm sure they thought that all sounded nice, but it telegraphed a cultural weakness and the Muslims didn't waste any time exploiting it.
We should have stayed out of Europe during the World Wars and let Germany dominate the continent.