Did a lot of British immigrate to the middle east during the imperial occupation and did there descendants?
There was never a significant level of emigration from Britain to its territories in the Middle East, so the numbers would be very small. The British relationship with Palestine and Transjordan was not really explicitly that of an occupying power, nor was it ever really seen as a possible new home for people from Britain. In fact the UK saw its role in the Middle East as that of administering territories under a UN mandate, so there was no incentive for people to move there from Britain. There was some immigration of Jewish people from Britain at the end of the mandate in 1946, however – but that had more to do with the creation of Israel as a Jewish homeland than owing anything to the specific involvement of Britain as the imperial power.