I think there used to be a name for a particular polling effect in the US where black candidates did better in polling than in actual votes.

Here it is: https://en.wikipedia.org/wiki/Bradley_effect

Which some theorized was based on the Social desirability bias https://en.wikipedia.org/wiki/Social_desirability_bias

In the US, the media tends to be biased against conservatives, and the little I've seen of the BBC, it's even more biased.

With such a media bias, I'd expect conservatives to tend to poll lower than the election results, particularly from polls from the media orgs, who tend to predict according to their own biases.