"Yemen" did not exist as a country until 1990. Prior to that there was North Yemen and South Yemen, with North Yemen being largely independent (and Marxist) from 1918, and South Yemen (where the largest cities of Aden and Sana'a are located) being a British protectorate from the late 1800's until 1962.

So I think to get a high-quality answer, we need to understand your question better. By "Yemen" do you mean the independent North? The British protectorate South? The Yemeni people? Or how the British used their remote colonies in the war effort?

Tell us more details about what you are specifically asking to know, and we may be able to provide something more in-depth than this precis of the Brittanica article: https://www.britannica.com/place/Yemen/The-age-of-imperialism#ref45274