One way or another the British were going to bail out of Palestine. There were far too many reasons they wanted out to list here. The entire problem was dumped in the lap of the UN, and in 1947/48 the UN had very little (if any) experience with peacekeeping, and not a lot of cash to pay for that. The third world militaries that do a lot of the "contract peacekeeping" now did not even exist in 1947/48. Nobody in Western Europe would have been happy to see troops from communist countries (still occupied by the Red Army) "volunteer" to go as peacekeepers, and the western European countries that had militaries capable of being deployed both had no desire desire to do so, and in many cases were involved with dealing with insurgencies in their colonies (North Africa, Indonesia, Vietnam, etc).
Absent a partition plan the British will give a pullout date and wash their hands of the situation. There will be rounds of tut-tutting as the situation devolves in to civil war, as it did OTL. At some point the fighting stops as the two sides reach a military stalemate. I expect the Israelis do somewhat better than OTL if there is less external pressure for the final cease fire as there is no official division of the space. Jordan will still incorporate those bits of Palestine on the West Bank they occupy. Egypt will incorporate Gaza, and to the extent Lebanon or Syria occupies anything over the old borders they will do likewise. After some interval those countries that recognized the State of Israel will do so.
Since there was never a partition plan, never an "international" Jerusalem, etc discussions about borders based on those plans will never happen. Naturally there will be Palestinian irridentism but from the start there will be no "return to partition borders" but a straightforward "one state" solution, for a "multiethnic" state, of course based on only those there before 1948 or some earlier date having a right to be there.
Like OTL you won't see a Palestinian state created from the parts of Palestine occupied by Arab countries/armies at the end of the fighting. That was doable in 1948 and at any time between 1948 and 1967 and it never happened for lots of reasons. Jordan and Egypt only gave up "Palestinian" territory after 1967 to a "Palestinian State" when they no longer occupied that land, it is easy to give away what you do not control. IMHO if the Palestinians/Arabs accomplish their purpose and throw the vast majority of Jews in to the sea in 1948 then maybe, just maybe you see a "Palestinian" state, but even then do not bet on it being the pre-1948 boundaries of the Mandate or controlling the Al-Aqsa mosque - that will probably fall to the Hashemites.