They didn't. The UK had abstained in the 1947 partition plan vote, officially handed some things off to Israel after independence (though most of the time they simply pulled out before independence, they did do official hand-offs to Israel), and was neutral during the 1948 war.

Hey, /u/uojosh - I've removed the question for being... well. A bit unanswerable! Britain was neutral during the 1948 War, so our experts are a little stumped on how to answer your question interestingly. We often find in these types of situations when our experts don't answer, that random splunkers will dive in and give the strangest, randomest answers possible (which helps no one, really).

Could you repost the question for me? Something like "During Israel's War of Independence in 1948, why did Britain choose neutrality over supporting one side?" I reckon you're going to get the answers you deserve from that, rather than the ones I'm only going to have to delete in here. =D