Depends on the comparison being made. I think one comparison between Britain and Israel that holds up is that, when I've asked for an explanation of why people think Israelis would never be able to identify with Palestinians instead of their own ruling class, the only actual answer I've ever got is a sort of soft-third-worldist one, that Israelis benefit too much from imperialism and inequality to want to give it up. I think it's worth pursuing that line of thought/questioning, because I'm not sure that Israel is a bigger player in imperialism or benefits more from it than the UK does.
Aside from that, there is also one corner of the territory ruled over by the British state where we could maybe make a more direct comparison. I don't claim to be a great expert on the Six Counties or anything, but I reckon that, even if it's perhaps less the case now, there's definitely been times in the relatively recent past when it's been hard to imagine what Protestant and Catholic workers could have in common with each other. But I think there are still common interests there, just as there are in the even more fraught Israel-Palestine situation.
As for the other bit - as I've explained, I was thinking as much about "why Israelis might be able to identify with Palestinians rather than the national interest" as with the same question for Palestinians, if not more so. But I think it's a bit weak to just shrug off any possibility of critiquing nationalism among Palestinians as well - a people who are oppressed can react or resist in all sorts of ways, some of them more nationalistic, others less so.