On the British withdrawal from Aden, Without Glory In Arabia gives a good insight into the politics surronding the events – but also gives a lot of space to the first-hand stories of British soldiers who were there at the time.
There’s also Britain’s Withdrawal from East of Suez, a more thorough and academic study.
But for a wider history of oil, the west and the Middle East, you cannot do better than David Yergin’s The Prize, a book published in 1990. It was made into a really excellent 8-part documentary series, handily available on YouTube. Here’s episode 6 on the 1960s.