They did. After the fall of the Ottoman Empire in the First World War, the entire area was British overseas territory. They named it Palestine as this was a non controversial name (at the time) until at least 1948. The pan-Arabic identity is a later addition and made far more complicated after the Six Day War.

After WWII Jewish people also moved to the US and the U.K - that’s why there’s a diaspora and fairly large populations in cities like London (where I live) and LA and New York.

Block me if you want, many do - though if you have been studying Middle Eastern history for many years, none of this should come as news.