is it allowed for a palestinian-british from entering israel

Israel doesn't deny entry to anyone based on their nationality, ethnicity, or where they have been. If you have a British passport you are as British as David Cameron. You might be asked some questions at immigration - as any tourist might be - which you must answer truthfully and politely, no matter how silly or irrelevant they might seem. Assuming your purpose in entering Israel is for tourism, and you have nothing to hide, you will be allowed in.

thanks for your reply

Israel doesn't deny entry to anyone based on their nationality, ethnicity

Well that's certainly debatable. You don't see a lot of people traveling between Gaza or Damascus and Tel Aviv these days.

You'll be fine entering Israel with a British Passport though.

You can certainly expect to be asked lots of questions at passport control, and you might be taken aside and questioned. That could take quite some time, but you shouldn't have any problems getting in.

letemspeak--Syria would not allow anyone in with an Israeli stamp in their passport. Israel DOES allow people with Syrian stamps to enter. There are no direct flights but it is possible. BTW do you realize how many Syrian victims of the Civil War have been treated in Israeli hospitals? Gaza is right now closed. People can enter and leave via Egypt ( if Egypt allows) Also, people are allowed out for humanitarian reasons. There are many Gazans being treated in Israeli hospitals.

they will get in, unless they are on 'the list'. And how are the Israelis going to know if the British passport holder is Palestinian in origin if they don't decide to tell them on arrival (unless they were born in like Tel Aviv, Tulkarm or Jericho, in which case it will appear as their place of birth on their passport).

Israel doesn't care that you are of Palestinian origin (which I assume means your parents or grandparents were born in what is now Israel or what is now the Palestinian Authority). That is no reason to deny you entry.
As long as you are not a known political activist, or are suspected of wanting to cause trouble (for instance, if you were to turn up at Ben-Gurion Airport immigration waving a banner in support of Palestine), your parents' place of birth or your ethnic origin don't matter in the least.
You might have a very obviously Arabic name. But so do thousands of Israelis (one-fifth of Israeli citizens are Arabs).
If you are visiting Israel for tourism, to see the holy places, to pray at Al-Aqsa, etc., you will be like thousands of others and that is no reason for you to be denied entry.
If you are asked any questions, just answer them truthfully and politely.
Have a great trip.

Well, I have a similar questions. My partners father was palestinian and my partner holds a palestinian name but is German (born here) and doesn't even speak arabic i.e. has no connection to his fathers family. Could this be a problem entering Israel. I think not but he is a bit worried.