Yes, in the UK this is called the "Shy Tory" effect. I don't think all the media here is biased against the Conservative Party (some are pro, some are con) but you are quite right that the BBC (which is easily the largest and most powerful media organisation) is hostile. It's possible this is (part of) the cause of this effect, and it's notable that the three general elections where the polls messed up all did so by underestimating the Conservatives and overestimating Labour.
But I don't know that this is a case of the polls getting it wrong. If this was a case of the "Shy Tory" effect, why did the exit poll (and the unpublished Survation poll) get it right? By comparison, in 1992 the exit poll was wrong.
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Whilst the BBC may lean towards the left and be a powerful organisation, I doubt that the effect it had was anywhere near as great as the combined forces of the Daily Mail, The Sun, the Daily Telegraph, and The Times. These newspapers, which account for a huge percentage of the UK's circulation, conducted what I can justifiably describe as a co-ordinated campaign of vitriolic rhetoric against the Labour party and Ed Miliband's character. It's telling that 2 of the 4 are owned by Rupert Murdoch, who has a lot to gain from a continued Conservative government.
There is simply no way the BBC would be able to pull the same kind of trick, as their reputation rests on them at least appearing politically neutral. It can't have been that hard to come up with some derisive slogan regarding the welfare cuts Cameron is inevitably going to try and make, but the country (both left and right) would be up in arms if it was seen to be the opinion of the BBC. The only left-leaning newspaper with a comparable circulation is the Daily Mirror, which ran the headline "Keep Cameron Out". I haven't seen this article myself, but I doubt it has the same attacks on character as the right-wing papers.
I'd be grateful if someone could give/suggest a reason for the downvotes.