The Balfour declaration was from 1917. But the Zionists first started to move to the region in the hopes of establishing a homeland in the early 1880s, based on their belief that a Jewish state (anywhere; Argentina was another candidate) was necessary for their long-term survival due to the long history of antisemitism in Europe - getting worse by the day - and their (correct, it turned out!) fear that it could reach cataclysmic levels. It was very much their idea.
Balfour's declaration, which wasn't official law, didn't single-handedly dictate British policy for the next 30 years and 14 governments; people vastly overstate the importance of it. Britain did not "ship out" the Jews - most Jewish migrants to Mandatory Palestine were from Eastern Europe and came to Mandatory Palestine very much of their own volition, without British help. And in 1939 - just in time for the Holocaust - Britain cracked down hard on Jewish migration to Mandatory Palestine to try to quell Arab unrest; Jews continued to migrate illegally anyway, despite what the British wanted.
Of course Britain had its role in contributing to the violence in the region, but to characterize Israel as a British colony is to deny Jews agency. It is curiously antisemitic, even as it (implicitly) absolves them of some of the blame for how things have gone.