Why did Britain want some kind of Middle East defense organisation during the British Empire era?
The desire for regional defense organizations only arose after the British Empire no longer had direct control over the Middle East. Before WWII, the British had no desire to have regional defense organizations because they were willing and able to simply defend the region on their own without having to cooperate with any of the countries of the region.
After WWII, this situation changed. Now, Britain wanted and needed to seem more like a partner and less like an imperial power. At the same time, however, they wanted to maintain influence in the region. They particularly did not want to "lose" the region to the Soviet Union since this was early in the Cold War. For this reason, the British tried to create regional alliances sort of like NATO. This was only partly successful as the British were able to create the Central Treaty Organization but were unable to get Egypt and countries in the Mediterranean area of the Middle East to join in any alliance with them.