The answer to this depends on your perspective on the Israeli-Palestinian Conflict.
The biggest mistake the Great Britain made with respect to the administration of the Mandate for Palestine was the issuing of the 1939 White Paper barring Jewish immigration to Palestine. It was a failure and a disgrace on all accounts. First, it showed that the British were willing to give in to Arab pressure. It was this belief that would eventually give Gamal Abdel Nasser the gall to nationalize the Suez Canal and provoke conflict with the British. Second, it was a complete about-face of British policy. Prior to this point, it was very clear from the Balfour Declaration and the terms of the British Mandate for Palestine that the area would be given to a Jewish State. Third, the period from 1939-1946, when the White Paper had effect was the time in history when Jews most needed a place to flee to. By upholding the White Paper, the British prevented Jews who could have escaped Europe from finding refuge. Tens of thousands of Jews may have been spared from the Holocaust if they could have arrived and settled in Mandatory Palestine. Finally, while the Arabs would continue to have an antagonistic relationship towards the British regardless of what they did, there was no reason to antagonize the Jewish Settlers who were pro-British for the most part. By approving the White Papers, the British cast their position with the Zionists into doubt with no serious diplomatic gain from the Arab side.