Indeed, the bottom line is that Palestine belonged to the Palestinians. It did not belong to the British, the League of Nations, or the UN. None of them had any authority to give it away.
"Palestine" belonged to ALL the Palestinians, not just the Arab ones. The Jewish peoples existing claims and rights were acknowledged by the international community.
Note: Britain, the League of Nations, the UN did not GIVE or GRANT rights to the Jewish people, they simply acknowledged the Jewish peoples existing rights. It was no different than the British or the French, the League of Nations, the UN recognizing the rights of the Syrian people, the Lebanese people, the Iraqi people, the Jordanian people. (And, for that matter, the Indian people, the Pakistani people, the Bangladeshi people, the Serbians, the Czechs, the Bosnians, the Croatians, the Koreans (N and S), Vietnamese, South Sudan, Belarus, Montenegro, Timore-Leste, or any of dozens and dozens of new nations which have come in to being in the past century).