I think that is probably true Combustible.
But in these turbulent days, a 'cultural liberal' bias is very, very different from a political bias. Many young people (incl. BBC young people) deplore politicization in any form (which makes me want to cry).
Though in some respects, a depoliticized but educated youth is precisely who should be moving up the ranks at the BBC. In News, anyway.
My experience of making documentaries for the BBC (as a freelancer) is that, when we're talking more generally and not confining ourselves to News and Current Affairs, the liberal, um, starting-point of those who hold real decision-making power only goes so far.
After several culls, there are few in the BBC who don't, at the first sign of trouble, jump to march to the beat of the market.
That is the problem - not liberal bias, but a commercial bias towards the greatest market share. Which, ultimately, is never liberal.