People aren't forced to pay for the BBC though. Public funding is through a TV licence rather than tax, with the licence being "required" only if you watch live TV or use the BBC streaming service.
Given the other streaming services available it's very easy to watch TV without it. I've never paid.
Not really sure why skewing left would improve trust ratings either, unless you're suggesting that people on the right don't trust any media, or only trust media that is right wing coded. The BBC is definitely not a left wing outlet by the standards of the UK.
Yes, the UK is slowly backing away from enforcing the license fee (they also talk of decriminalization), partly because the immorality of it is clear to everyone and because those who don't care for it are now in the majority.
Nonetheless, there's no reason not to go all the way. There should not be a TV license, let alone one enforced by criminal law. Regular subscription and video scrambling systems are enough and have been for years.
The BBC is very strongly left wing and even its own employees recognize that. Look at the positions they take on a wide range of issues and you'll find they're all Labour positions or to the left of Labour.
I wasn't even talking about enforcement, I neither pay nor fall afoul of the terms.
I can't find any evidence of BBC employees calling it "far left", all I find when searching for that is right wing people calling it far left for not agreeing with them enough as well as some more "scientific" analysis that seemed to show it having a right wing bias. Most news bias raters put BBC as centre or centre left (it probably is centre left by US standards).
Looking at the top 3 stories now, two don't have any obvious political slant, Australian elections and arrest of terrorism suspects, whereas the 3rd is about local elections and starts with lots of quotes from Reform UK about how well they're doing. Perfect opportunity for a far left org to insert criticism, downplay, or just not report on them, but seems like pretty straight down the middle reporting.
But as you just discovered, there are endless examples.
Dismissing criticism of BBC bias as "right wing people calling it far left for not agreeing with them enough" is almost tautological: yes, that's what bias looks like, the people it's biased against will disagree with them a lot. Not because they're just wrong and the BBC is just right, but because the BBC fires right wing journalists and hires/promotes left wing journalists who then tell themselves that left wing beliefs are True and right wing beliefs are False and thus the news should automatically be left wing. It has been like this for years.
A few more simple examples of institutionalized bias:
1. During Brexit Nick Robinson wrote an article saying the Today programme no longer has any obligation to balance its coverage of Remain vs Leave; i.e. stating in public writing that the BBC is biased.
2. Many on the right don't believe climatology is scientific or accurate, but the BBC has a written policy of refusing to interview or platform such views. They just systematically forbid it and have done for decades. They only report the left's view that there is a crisis. That's political bias.
3. The BBC broadcast a documentary about Palestine in which the child narrator turned out to be the son of a Hamas official.
4. BBC on the US election: "On the campaign trail, Donald Trump drove his message of fear all the way to the White House but it was based on a misconception. Rather than an invasion, America has long been dependent on the work of these migrants in agriculture and manufacturing, making them both essential and dispensable…For his opponents these feel like dizzying and dark times."
Of course if they discover they have a journalist who criticizes the left they fire him immediately citing neutrality (see Chris Middleton).
All this makes a mockery of the concept of public service broadcasting. The BBC is gonna die, it's inevitable, and when it does, it will be because its staff relentlessly abused the public for decades by exploiting the tax based nature of its service.
Not really sure why skewing left would improve trust ratings either, unless you're suggesting that people on the right don't trust any media, or only trust media that is right wing coded. The BBC is definitely not a left wing outlet by the standards of the UK.