It didn't belong to the British. They were granted the responsibility (by the LoN) to administer Palestine as a class A mandate to bring it into statehood and independence. If you ever take the time to see how the UN surveyed the land when they were considering partition, you will see how much was considered Arab land, and how much was considered Jewish.
It did belong to the British.
They conquered it from the Ottoman empire in 1917 and instated Martial Law for 3 years before it was declared a British mandate by the LoN in 1920.
Regardless, it was theirs no matter how you look at it, it wasn't given to them, they already had it, it was just cheap politics.