As far as I know (and different from the US), they are strictly apolitical entities that have to make their decisions based on population figures and existing geographic and administrative boundaries.
However, the constituencies they’ve created tend to be to the advantage of Labour and to the disadvantage of the Tories and especially the Liberal Democrats. For instance, if I feed Electoral Calculus 30% Labour, 30% Conservative and 30% LibDem, it predicts 306 Labour MPs, 210 Tories and 102 LibDems.
There are two possible explanations for this: Either the Boundary Commissions are full of secret Labour supporters who do whatever they can to create favourable constituencies, or the rules for creating constituencies are such that the result will favour certain parties.
I would disregard the former of these – there’s no way the Tories and the LibDems wouldn’t hear about such a plot, especially given that the Conservatives were in charge when the penultimate review was conducted.
So what is it about the rules that make them favour Labour and to a certain extent the Tories?
It’s probably the idea to align the constituencies with administrative boundaries.
Because of the size of typical British council areas, this means that cities will be split into city constituencies that are likely to vote Labour, and that the suburbs will be merged with the surrounding countryside, creating constituencies that are likely to favour the Tories (at least in England).
If instead constituencies were supposed to contain an equal mix of countryside, suburbia and city, Labour might suddenly be severely disadvantaged.
Some people are suggesting that the Tories’ idea to create larger constituencies by reducing the number of MPs is designed to get rid of the Labour advantage. I haven’t seen this fleshed out anywhere, though, so it might just be wishful thinking.