Britain (like others) has found itself in many difficult positions. Whenever a Controlling force withdraws the various parties will vie and fight for position. India for example, Yugoslavia another. The same applied to Palestine.
The earlier part of the Bard response read ...
"Late 19th century: The Zionist movement, which advocated for the establishment of a Jewish homeland in Palestine, began to gain momentum.
1917: The British Balfour Declaration pledged British support for the establishment of a Jewish national home in Palestine.
1920-1948: The British Mandate for Palestine was established, giving Britain control over the territory. During the Mandate period, British policy was largely supportive of Zionist goals, and Jewish immigration to Palestine increased significantly.
1947: The United Nations General Assembly passed Resolution 181, which called for the partition of Palestine into two states, one Jewish and one Arab. The Palestinian Arabs rejected the plan, while the Jewish community accepted it."
The 1947 comment is interesting as it has fully reversed ... now the Palestinian Arabs accept the two state solution in principle but Israel does not. Oh the wheels of diplomacy and politics!
I cannot and will not comment on the position pre 1948 as I have no knowledge of it but it seems to me Britain was damned if they do and damned if they don't. If they had tried to retain control they would have been accused of colonialism and if they relinquished control as they did they can be accused of causing the current dilemma by allowing Israel to self determine and self declare the formation of their state and claim the lands they wanted.
Maybe the Palestinians should have agreed to the original British proposal of two states but they probably saw the country being surrounded by Arab nations and felt they had the upper hand. But then overnight after Israel made it's declaration of UDI the USA recognised the formation of the state of Israel and the balance of power changed instantly.
The fight for the formation of the state of Israel is historically depicted in the film Cast a Giant Shadow (https://en.wikipedia.org/wiki/Cast_a_Giant_Shadow), well as historical as Hollywood can be! The scene I remember most is when Jewish boat people (yes, they had them then!) were depicted arriving on a beach in Palestine and being confronted by British forces who ordered them to turn back, they didn't, so a volley was fired over their heads ... they still didn't move. The British officer remarked (for the film) "why don't they turn back, do they want to be shot" to which his colleague remarked "they have nowhere to go sir"!
Maybe the British could have/should have handled it better but things can always be handled better with the benefit of hindsight and the removal of pressure from all vested interests. Yes it could be said the British were responsible for the handover as it was but they were not helped by America's instant recognition of Israel allowing them to claim the lions share of Palestine.