Bruce polling for several years shows consistently that being neutral or pro-Palestine (or don’t know) in this conflict is consistently higher than being pro-Israel (which even now after Oct 7th and months of daily coverage is a position that less than 20% of people hold):
Thinking only of the continuing conflict between Israel and the Palestinians, do your own sympathies lie more with the Israelis or more with the Palestinians?
yougov.co.uk
Yes, the conflict itself not an issue itself that the vast majority of people care about - but what motivates our politicians is something people care strongly about.
Why do so many of them take such a strongly pro-Israel line?