In Palestine

No. The British Mandate for Palestine wasnt really a colonial project, except insofar as the Mandate incorporated the Balfour declaration and was therefore tied to Jewish settlement and the Zionist project. (Tied to, but not always or necessarily supportive of.) There were British nationals among the Jewish residents of Palestine of course, e.g. Chaim Weizmann, who became Israel’s first President. These residents became citizens of Israel after 1948.

In British Palestine, today's Israel, West Bank, and Gaza, there was no attempt to settle ethnically British civilians in the area in any sustained fashion. The British interest there did not require it, and they had quite enough to deal with during the relatively short period they held it (1918-1948, roughly), given the second world war and the leadup to it as well as the general decline the British empire faced following it, and the riots and tensions among Jews (and Jewish immigrants) versus Arabs in the area.

British Jews arrived, but there was no real movement by the British government to inspire British Jews to arrive. While they were at time supportive and opposed in alternating intervals to Jewish immigration, it was never tied to the Britishness of those immigrants really.

That's not to say there were no British civilians there, but to call them "settlers" would be misleading. But the Mandate's ultimate goal called for eventual self-governance and for a Jewish homeland in the area (it incorporated the Balfour Declaration), so settlers were superfluous and contrary to the Mandate's idea. The British did waffle on the idea of a Jewish national home, saying in the Churchill White Paper of 1922 that they did not mean for one to be established in the "whole of" British Palestine, but it also muddied the waters on what a "national home" meant, implying it didn't necessarily mean a state. Even so, the British were quite clear from the start that they had no interest in keeping control via the implanting of British citizens in the area.