Marx pointed out that communism could easily be presented as Christian and the mainstream churches are mostly Left-leaning. Even Papal encyclicals make some concessions to socialist thinking. See both "De rerum novarum" and "Centesimus annus".
In that context a recent report from Britain is not inherently surprising. The Guardian summarizes:
People with faith are far more likely to take left-of-centre positions on a range of issues, including immigration and equality. The research, revealed in a new report by the thinktank Demos, undermines the widely held view that members of religious groups are more likely to have conservative tendencies.
The Demos report suggests that the example of the outgoing archbishop of Canterbury, who combines deeply held progressive beliefs with his religious convictions, is not unusual.
"Rowan Williams may be far more representative of the religious community than many have suggested," said Jonathan Birdwell, the author of the report. "Progressives should sit up and take note. Their natural allies may look more like the archbishop of Canterbury than Richard Dawkins."
The report found that 55% of people with faith placed themselves on the left of politics, compared with 40% who placed themselves on the right. The report also suggests that people with faith are more likely to value equality over freedom than their non-religious counterparts. It discloses that 41% of people with religious views prioritise equality over freedom, compared with 36% of those without faith.
The report, based on an analysis of the European Values Study, also finds evidence that people who belong to a religious organisation are more likely to say they are very interested in politics, to have signed a petition and to have participated in a demonstration.
There are some large caveats to be attached to that report, however. England is generally an irreligious country and the survey was based on the 13% who report that they belong to a church. It did not ask which church, how often the respondents went to church, or how strong are their religious beliefs. Usual Sunday Attendance at church in England is less than one million out of a total population of about 55 million -- which is about 2% (to be generous) -- so we see some gap between the 13% and the 2%
And even that 2% is no indication of religiosity. Attendance at the Church of England in particular is often motivated by broadly social reasons rather than by any real religious convictions. And any influence the C of E had would be of a Leftist character -- as is shown by their totally unbiblical acceptance of homosexual and female clergy.
So what does the survey tell us about religion in Britain? Very little, I am afraid. It's entirely possible, though not probable, that all the genuinely religious people in England are conservative.