According to the biography of Reb Yosef Chaim Sonnenfeld, the Agudah in E”Y was working very hard to get frum Jews from Europe to move to Eretz Yisroel in the years before WWII. They were severely limited however, because the British recognized the Ben Gurion’s group as the official representatives of the Jews and all visa’s had to go through the Hagana. The Hagana did not want “old fashioned” Jews coming to E”Y so they gave the Agudah very, very few visas per year. Eventually the British themselves severely limited all Jewish immigration to appease the Arabs.
There is a myth out there that Jews could easily just go to E”Y if they had wanted to before the War. It is a gross oversimplification and far from the truth.
I should point out that the Agudah’s motivation was not to save Jews from Hitler. Their motivation was to combat the growing numbers of Chilonim with numbers of their own.