Disclaimer: I work for the BBC.
The BBC doesn't have 'a clear political affiliation', and neither does Channel 4. Both are public service broadcasters that are committed to non-bias reporting. However, they are run by people, and people are bias.
It might be because a right-wing government is more likely to make cuts in funding of a public broadcaster than the left. I have not thought the reason why it is in depth though. I wonder if you have an opinion?
Note that this is not an absolute endorsement of liberalism; change can only be positive if people are properly informed, and doing it for the right reasons. And, well, they aren't - not for some time now. And it's been hijacked by identity politics (some is very good; some very bad, more to do with narcissism than anything else, sigh)