Well, you're partially right and partially wrong.

Most authors break it down this way:

1. It was, at least at the start, an idea for solving the "Jewish question". Anti-Semitic British politicians would support it because it would provide a way to get rid of Jews that they simply couldn't, or who wouldn't, be assimilated into British society.

2. It was, at least partially, motivated by Jewish contributions to the British and personal relationships. Chaim Weizmann, Israel's first president and one of the most ardent pushers of the diplomacy route to try to establish Israel (and, in my opinion, the second-most important Zionist behind Herzl in establishing the state) was a very devoted man. He sent out hundreds, if not thousands of letters, constantly attempted to get support, and did quite a bit of diplomatic bargaining to get himself into the position to influence major world players. His influence was so great that he often intervened personally with Truman to try and convince Truman not to alter things like the partition plan to exclude the Negev, for example. He was a chemist by profession, and provided a significant contribution in acetone production (if I'm not mistaken), which helped the British manufacture ammunition greatly, and his work convinced many British politicians as well.

3. The British did have some ethical considerations, notably after the Holocaust. Though the British attempted to avoid influencing others or taking sides in the conflict after WWII, and indeed committed some very cruel acts (ie. the turning away of the Exodus, a ship filled with Holocaust survivors who were not allowed to embark in Israel, and instead were sent to France who refused them or they refused, then to Germany), there was still sympathy for the plight of the Jews among British politicians. It wasn't entirely about strategic gain, though there was indeed that consideration!

4. The British had political influence in the Middle East, but they hoped to gain more. The original Balfour Declaration was intended in part to establish a small Jewish state somewhere in the Middle East, but this wasn't necessarily for the Jewish state to help. It's actually thought that, at least in part, it was intended to shore up support for the Russians, whose Jews would presumably try to keep Russia in the war instead of falling to the Russian revolution as it did, so they could help Britain and help the establishment of a Jewish state. This, along with other strategic considerations (ie. shoring up Jewish support at home, attempting to ensure that a friendly group was in control of an area that would be needed to connect Britain to its oil supplies in Iraq) led to British actions throughout the period as well.

All of these considerations and more led the British to support the Jewish state until roughly the start of WWII, when one can see a shift (to a small degree) away from the Jewish cause with the White Paper of 1939. However, the support didn't really disappear, it still was seen in subsequent actions (Churchill, for example, noted the support while also noting it might be taken away after the assassination of Lord Moyne in 1944 by the terrorist Zionist group Lehi), but the British were weary of the fighting and were hoping to get out by 1947 as quickly as possible. So they not only refused to influence other states on the UN Partition Plan vote, they abstained themselves, hoping to avoid any further conflict they might end up involved in that would cause them to lose any more diplomatic face.

British control in the Middle East, therefore, wasn't the only consideration at play. However, shoring up that control, and attempting to walk a tenuous line of keeping Russia in WWI while helping the Jews while getting rid of the Jews while trying to keep strategic control of the route to Iraq all had a hand in British considerations, not all of which (obviously) panned out very well.