I don't know about the most recent BBC report, but I'm aware of some earlier research by independent academics from Glasgow uni
Bad News From Israel by Greg Philo et al.
http://www.gla.ac.uk/centres/mediagroup/badnews.htm
It kind of bust apart the assertions that the BBC has an anti-Israel bias, because if anything, it showed the reverse, it gave Israelis more airtime, and there were discrepancies in reporting, i.e. Israeli attacks on Palestinians were usually shown as retaliation, whereas Palestinian retaliation was usually shown as an attack, i.e. reports usually went along the lines of Palestinians attack, Israelis retaliate; they didn't intermittently flip over and report Israelis attack, Palestinians retaliate. (I purposely worded it like that, not intending to take one side or the other, but to highlight the chicken:egg nature of the attacks:retaliations.)
Like I said though, I don't know the results of the more recent BBC study. I can imagine either way it would be harmful:
* if it showed a pro-Israeli anti-Palestinian bias (i.e. if it came up with similar findings to the Glasgow study), then that could be tricky. I wouldn't want to be Alan Johnson if the BBC is reported conclusively to be biased against the Palestinians.
Alternatively:
* if it showed a pro-Palestinian anti-Israel bias, then the BBC would get more hate mail from American Zionists than it already does.
And while I don't have a clue about the contents of the report, and I'm just guessing, given the earlier findings of the earlier independent study, and given how difficult it is to report from the West Bank and Gaza, I'd be guessing the latest report, commissioned by the BBC, probably shows more of the same, i.e. pro-Israeli bias, but I might be wrong.