The British wavered in their level of support over time, to be fair. Indeed, the British Prime Minister at the time of Israel's creation was not considered to be heavily in favor of a state, and the British abstained in the UN General Assembly vote that recommended partition and the creation of two states. Clement Attlee, the British Prime Minister from 1945 to 1951, was widely regarded as a foe of Zionism despite earlier statements supporting it. However, he also took a backseat in foreign affairs, often deferring to his foreign minister, Ernest Bevin, who was prone to anti-Semitic comments and cared little for Zionism himself. Bevin and Attlee restricted Jewish immigration, and Bevin was quite clearly opposed to a Jewish state, preferring to establish an international trusteeship that would eventually turn into a single, Arab-run state by virtue of demographics.

The US was also divided in a sense, given the State Department's opposition to the creation of Israel, but President Truman was in favor of Zionism and there were voices in favor as well.

Why did they stick to the idea of partition? Because, unlike the statement you made at the end, Jews were part and parcel of the local population. Short of expelling the 600,000+ Jews in the area by 1947, who made up over a third of the population, and preventing any further Jewish immigration of the many who wanted to arrive there, a single state was argued to be insufficient. Such a state would not have guaranteed Jews their right to self-determination, which leaders argued would lead to continued conflict. Furthermore, such a solution would have meant a failure for one particular plan, which was to solve (or at least alleviate) the problem of Jews living in displaced persons camps following the Holocaust who could not conceivably return to homes either destroyed or given to non-Jews following their fleeing/expulsion/internment. The US and UN and British were all acutely aware of this problem, which was part of why further Jewish immigration was a very contentious topic; it would have further entrenched the Jewish population of the area and also inflamed Arab passions further as a result. Ultimately, a Jewish state alongside an Arab one was judged to be the only one that would preserve the rights of both peoples to self-determination, despite opposition to such a solution by the Arab populace, because the Arab populace's opposition to a Jewish state was seen as an outcome that would be far more harmful to one side than it would be fair to both.