Yes the British Empire (along with France) has done unspeakable damage to the middle east; damage that is felt to this very day. However blaming the Brits for doing stuff 80 years ago isn't going to help anymore. Also twisting the historical facts that led to this conflict (like you just did) doesn't help either. How the UN would've partitioned the land is irrelevant because at that time the Arabs in Mandatory Palestine and in bordering countries did not condone the idea of a Jewish state in any boundary whatsoever. Moreover, the Arab states did not attack Israel to "free Palestine" (meaning to establish a Palestinian state) but to take the land for themselves. Further proof for that is that the West Bank and the Gaza Strip were Jordanian and Egyptian territories respectively until 1967 yet they did not establish a Palestinian state. Not only that, but the PLO (the Palestinian Liberation Organization) was established in 1964 when there was no Israeli occupation in the West Bank nor Gaza whatsoever (you can try and guess what they actually wanted to "liberate").

You also failed to mention that many Israeli Prime Ministers (both left wings and right wings) have tried to negotiate with the Palestinian but failed. The worse of then all was the Oslo Accords and then later the Camp David talks that eventually collapsed due to an intentional and planned uprising (the second intifada) by the Palestinian leadership.

But even after that, Israel gave the entire Gaza Strip to the Palestinians, Jew free as they wanted, with no conditions as a solid step toward peace and that also blew up in Israel's face.

There's a good reason why over the years Israelis have been leaning more and more toward the right political spectrum, whether it be the Palestinian leadership unwillingness to compromise even a bit for peace or the endless terror attacks against innocent civilians by suicide bombers or rocket barrages.

To this day the Palestinians haven't returned to the negotiating table. They deliberately incites its population against Jews, glorifies terror attacks against Israelis and even pays salaries to convicted terrorists (pay for slay).

So saying that "yeah both sides are bad" is giving the Palestinians way too much credit that they actually deserve.