During the 1930, the British had control of Palestine, not the Palestinians. So if anyone at all opened their doors to jewish refugees, it would have been the British. But even them only let enter a short number of refugees (think of the 'Exodus'), which they didn't do out of benevolence but out of the unability to contol the situation.
Cease-fire breaks down in three areas in Syria, monitor says (Reuters)
from the article: Separation at the Erez crossing