Health,
The British only grudgingly wrote the Balfour Declaration due to the pressure the Zionists put on them, and because they felt it would further their relationship with the Wilson administration who’s top aides were Zionists. It would not have happened without the Zionists
The British didn’t write it due to any love of Jews and it doesn’t follow that they would have been happy to let masses of Jews emigrate to their colonies when every other country on earth found a pretense not too.