No, this is incredibly counter to historical fact. The zionist project began appropriation of Palestinian land even before the British mandate in 1917. The British helped accelerate this after their mandate, however. The displacement of Palestinians had grown so severe by 1936 that a large-scale armed rebellion was triggered (see Ghassan Khanafani's The 1936-39 Revolt in Palestine https://www.marxists.org/archive/kanafani/1972/revolt.htm for a bit of background).
Ultimately, the entity was wrested from British control through anti-English terror bombings.
That isn't to say that it doesn't serve English (and more broadly European) interests--there is a reason they supported the zionist appropriation of Palestinian lands. The British, and Europeans more broadly, wanted Jewish people out of Europe, and they wanted people they saw as expendable to be on the front-lines of colonial destabilization of Western Asia. Even the Third Reich supported zionist endeavours to relocate Jewish people to Palestine.
However it wasn't some English trap, nor was it done after the Holocaust. The zionists had historical agency and chose to embark on a settler-colonial trajectory long before the Nazis seized power, and they were willing to attack and alienate their British backers to secure their sovereignty and guarantee their place as the helmsmen of Palestinian colonization.