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 If this was a case of the "Shy Tory" effect, why did the exit poll (and the unpublished Survation poll) get it right?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.