’high profile’ Labour members with links back to the BBC include: Peter Mendleson (Media guru for Tony Blair with closer links to Greg Dyke (from LWT TV). Greg Dyke later become Director General of the BBC), Will Hutton (Guardian journalist to BBC Journalist), Liz Fogan (BBC and Guardian Journalist), Andrew Rawnsley (BBC to New Labour activist), James McNaughtie (Guardian to BBC staff Radio 4), (1997) Lance Price (BBC to New Labour activist), Martin Sixsmith (BBC to New Labour activist), Tom Kelly (BBC to New Labour activist), Ed Richards (BBC to New Labour activist), Bill Bush (BBC to New Labour activist), Catherine Rimmer (BBC to New Labour activist), John Birt (BBC DG to New Labour activist), Don Briad (BBC to New Labour activist), Sarah Hunter (BBC to New Labour activist), Ben Bradshaw, (BBC to New Labour MP 1997), Chris Bryant (BBC to New Labour MP), Celia Barlow (BBC to New Labour MP), James Purnell (BBC to New Labour Gov. Minster), Ken Macintosh, (BBC to (Scotland) MSP).
Right -- New Labour, Blair's people. All of them against an actual left-winger like Corbyn, because New Labour were not left wing barring some issues of identity politics. Economically, they were liberals, which is why Rupert Murdoch gave them his support, and why he and other media moguls despise actual left-wing politics that can change the economic status-quo.
Most of these "luvvie" types are just liberals when it comes to economics; neo-liberals who are big on gay rights and other issues of identity politics, that was New Labour. That's why they didn't do anything to regulate financiers and prevent the financial crash, on this they were the same as the Tories (who also called for less and less regulation of The City).
It's Neo-Liberal bias, not left-wing bias imo.