From my perspective the BBC is extremely anti-Israeli but for some people this is obviously not good enough. They want the BBC to champion their cause. Naturally people supporting the anti-Israeli cause who only get anti-Israeli content will feel that the BBC is "pro" Israel. Nothing could be farther from the truth and Pro-Israeli media looks nothing like the BBC.
This is from 2006:
https://www.bbc.co.uk/bbctrust/our_work/governors_archive/im...
"We were appointed by the Governors to assess whether the BBC's coverage of the Israeli- Palestinian conflict meets the required standards of impartiality."
...
"apart from individual lapses, sometimes of tone, language or attitude, there was little to suggest systematic or deliberate bias; on the contrary there was evidence, in the programming and in other ways, of a commitment to be fair, accurate and impartial;"
...
"these shortcomings include:"
...
"Equally in the months preceding the Palestinian elections there was little hard questioning of their leaders"
...
This has been a big criticism of the BBC which is still not addressed:
"The term "terrorism" should accordingly be used in respect of relevant events since it is the most accurate expression for actions which involve violence against randomly selected civilians with the intention of causing terror for ideological, including political or religious, objectives, whether perpetrated by state or non-state agencies."