Needs to be seen in the context of a country where far fewer people are seriously religious than in America; where under 15% attend church regularly; where a sort of vaguely culturally-Christian agnosticism is so common that it is almost impossible to get a sense of the respective proportions of believers and atheists in the country, and the distinction may be often irrelevant - many don't care enough to be explicitly either. FWIW, the percentages of Brits who claim to be atheist has varied in different recent surveys from 35% to 60%.
So by definition no such study can be entirely reliable. But it's true that the Christian left is far more pervasive here than it seems to be in America, and that the Anglican leadership, with some noted exceptions, is quite liberal. Maggie Thatcher found the bishops and other clergy a great nuisance, because they kept criticizing her economic and social policies; and David Cameron has been finding the same. Religious people have been very active in causes against poverty, social injustice and war.
That being said, there is also an increasing Christian-right element in some quarters. I think that it stems from two sources: the GAFCON rebellion against the liberalism of the Church of England leadership; and the fact that the internet facilitates contact between the American and British right wing. It is obvious that some of our more right-wing newspapers, since they went online, have been pandering to some degree to the American teabagger types as well as the indigenous Right, and this has led to some increased role for the religious right. I could a tale unfold about their pernicious recent political influences in the constituency where I live, Oxford West and Abingdon.
Nevertheless, most religious people whom I know personally, including Christians, Jews and Muslims, range from liberal to very left.
'Is the term Christian liberal about to enter our political lexicon?' In Britain, the term 'Christian Socialist' entered it in the 19th century!