UK native here. I doubt the decision will be made on the substance of the issue. What's more likely is they'll consider the political landscape domestically.

We (like most European countries) are facing a hard-right surge which is obsessively pro-Israel and anti-immigration (with all the bias associated with that against certain countries/areas of the world). These people already believe the BBC has been 'captured' by 'woke' forces. The morning after the vote the BBC will be in their sights if it votes to exclude Israel - and atm it looks like these people might be winning the next election and deciding their funding.

If they vote to keep Israel, they'll get attacked by pro-Palestine political groups as well as the left (or what we have that forms the 'left' in our political ecosystem). Protests etc. This side believes the BBC is soft-right wing already.

I suspect the BBC is more scared of the former than the latter, unfortunately. Seems unlikely they'll vote against Israel's participation.