I lived in the UK back during Brexit and the only people who said that “the BBC is Leftwing” were the English Far-Right - in fact that kind of stuff started (or at least became “mainstream” enough to be noticeable) at around that time and then was picked up by the Far-Right populist side of the Tory Party during the Leave Referendum.

They’re a posh kind of Rightwing, so far more subtle than loudmouths like Farage, Boris Johnson and Trump, but it didn’t take me long after coming to live in the UK (a decade before Brexit) to notice how much to the Right they were (not even Center-Right) from their fawning coverage of the Monarchy, almost invariably positive spin on the “upper” classes and the ultra-wealthy and heavy nationalist take on all foreign affairs (they almost invariably spinned it as “other countries are listening to Britain” when the same news in foreign media barely if at all mentioned Britain).

Certainly the core message from the BBC was always that “the System is good as it is, be proud of it” and “don’t make waves”, in a country which is highly unequal and has pretty low Social Mobility when compared to the rest of Europe.

Also remember how, well before they had any meaningful impact, the likes of Nigel Farage and Boris Johnson got way more airtime in the BBC than, say, the leader of the Greenparty.

Brexit didn’t happen by chance: the fields were Far-Right Nationalism flourished had been long plowed by amongst others the BBC.