> When papers like the Sun and Mail are the most popular in the UK I think it's hard to agree that Britain overall is left leaning
"Left leaning" is of course relative. Some claim that Tony Blair is right wing, and Corbyn is the "middle ground". If you claim that then sure Britian is overall right-of-corbyn.
But if you take the standard "Lab/Lib/SNP/Green" is left leaning, and "Tory/UKIP/BNP" is right leaning, then as the left have have a majority every election it's quite reasonable to believe what the facts say.
Take one look at the election results and you can see there is a constant majority that's "left"
A lot of the complaints stems from a perceived view that UKIP were overrepresented on Question Time in the run up to 2015. That's no defence for the claim the BBC is "pro establishment", as Farage and indeed Brexit was quite clearly anti establishment.