I'm going to counter-point that. While there is a lot of whinging on this thread that fits your model, it doesn't address the BBC's actual bias.The point I keep on making, you have your own bias at work. All of the complaints I've seen from left, right and centre have been because the presenter/program in question hasn't reflected the complainants bias. Obviously the left and centre complaints are from elsewhere.
It's a good example of social media echo chamber amplification. Anyone on here complained about AFNs grilling of Jezza?
That bias is not pro any particular party (though I suspect in the mid-late 90s it was very pro Labour, I was a kid then so wouldn't have been able to make a valid judgement and probably wouldn't remember it now). The bias is internationalist/globalist, liberal metropolitan elite.
To shoot down your Andrew Neill's execution of Corbyn, Neill also did a number of Farage (the polar opposite of Corbyn) as well as Wee Nicki and her from the Lib Dems. He would very likely have done the same to Johnson too (hence the discretion being the better part of valour) and I'd have applauded- doing over politicians is his job! The charges of bias do have grounding however in how certain high profile interviewers treat politicians from different parties differently. Marr being the worst offender for me (though Naga Muchetty is only a hair's breadth behind mostly due to her smug superiority) frequently giving an easy ride to the SNP or Labour talking heads, letting them speak at length while only peripherally (or not at all) answering the question that had been asked. Compare with the typical Conservative minister turning up on his show, and if their answer is longer than three words they are going to be interrupted. That is not "ensuring a satisfactory answer" and it is certainly not balanced.