The British were supposed to help the Jewish people re-establish their homeland, but instead of freely letting the Jewish People settle in their homeland, they placed restrictions on Jewish immigration while allowing Arabs to enter the country freely. Apparently, London did not feel that a flood of Arab immigrants would affect the country’s absorptive capacity, but the immigration of Jews would, now that is apartheid.
During WWI, the Jewish population in the British Mandate declined because of the war, famine, disease and expulsion by the Turks. Between 1915 and 1922 the population of Arabs grew by 53,000 and they were freely able to flood the British mandate while only Jewish population was restricted and only grew by 1,000 people.
Between 1917 and 1921 what is now Jordan was part of the British mandate. In 1920 the San Remo Resolution said the Jewish homeland was to be established in Palestine. The British stole 77% of the Jewish homeland and gave it to the Arabs. In the tiny bit of Palestine left the British continued to restrict Jewish immigration while Arabs were freely able to enter. In 1930, the Hope Simpson Commission, was sent from London to investigate the 1929 Arab riots. The commission found that the British practice of ignoring the uncontrolled illegal Arab immigration from Egypt, the newly formed Transjordan and Syria had the effect of displacing prospective Jewish immigrants. 
The British Governor of the Sinai observed: “This illegal immigration was not only going on from the Sinai, but also from Transjordan and Syria, and it is very difficult to make a case out for the misery of the Arabs if at the same time their compatriots from adjoining states could not be kept from going in to share that misery.”  In 1937, the Peel Commission found that the “shortfall of land is . . . due less to the amount of land acquired by Jews than to the increase in the Arab population.” 
With Jews being killed in the Holocaust do you think the British changed their minds and let Jews enter their homeland? No, many Jews fleeing Europe that went to the British Mandate were sent back to Europe to die. See the White Papers. After the war the British began to put those they caught in concentration camps in Cyprus. Of the approximately 50,000 people detained in the camps, 28,000 were still imprisoned when Israel declared independence in 1948. 
1)Arieh Avneri, The Claim of Dispossession, (Tel Aviv: Hidekel Press, 1984), p. 28; Yehoshua Porath, The Emergence of the Palestinian-Arab National Movement, 1918–1929, (London: Frank Cass, 1974), pp. 17–18.
2) John Hope Simpson, Palestine: Report on Immigration, Land Settlement and Development, (London, 1930), p. 126.
3) C. S. Jarvis, “Palestine,” United Empire (London), Vol 28 (1937), p. 633.
4) Palestine Royal Commission Report, p. 242.
5) Aharon Cohen, Israel and the Arab World, (NY: Funk and Wagnalls, 1970), p. 174.