That's really an article that's trying to spot vague trends in voting patterns rather than anything approaching proof that religious people vote along party lines. Yes, whilst there are some patterns that suggest that Catholics are more likely to vote Labour than for any other party, the percentage of Catholics voting Labour is still below 50% so most Catholics do not vote Labour. For Anglicans they're more Conservative, but again, below 50%. Muslims, Sikhs and Hindus are fairly heavily Labour although most people would say that's because Labour are typically more immigrant-friendly.

Here's a better source with some actual numbers included. Here is another - note the sub-heading "religious block votes do not exist in Britain".

Even if you could point to vague trends in who the religious vote for, the Atheist vote is equally spread - read this. So even if the religious were strongly affiliated, the fact that Atheists aren't would render that irrelevant. I'm an Atheist yet I'm also a floating voter having voted for the 3 largest parties on different occasions.

So I'm afraid that your argument that Atheists are Atheists because they don't agree with the politics of the religious, just doesn't stand up at all in the UK.

Personally I'm an Atheist because I don't believe in fairy tales.