Was it really self-harming to cut the colonies loose? What Macmillan did was basically say to Kenya, South Africa (and the Federation of Rhodesia and Nyasaland), and other states still hanging on to minority settler rule, that Britain was not issuing blank checks and would not support their increasing extremism, not after the incredibly expensive and horrific experience of fighting the Land & Freedom Army ("Mau Mau") to placate the settlers in Kenya and witnessing the disasters of Viet Nam and Algeria for the French (who were in the process of working towards their own climbdown in Africa). Basically it was meant to encourage such settler regimes to come to peaceful arrangements with the moderate nationalists and not force the issue into violence. Britain, after all, could not coax the Commonwealth to support them on any such action, and they simply couldn't pay to hold the colonies by force. I am not sure how true the comment is that the US also encouraged Macmillan to take his stance for Cold War related reasons--to defuse the liberationist appeal of the Soviet bloc and communism generally--but it would not surprise me given the way Macmillan thought about geopolitics.

By the time Macmillan made his tour, in fact, a variety of African (non-settler) states that would become independent in the years to come were already under significant self-government. Ghana was already independent; Sudan had been negotiated in 1952 (for 1954); Nigeria was already devolved into local African government in the provinces and in November 1960 got a black Governor-General in Nnamdi Azikiwe. Tanganyika had elections in 1958 and 1959, with local self-government due for 1960. The point therefore did not come out of the clear blue; Britain was already making moves to peaceful devolution, but arguably the Wind of Change speech and tour were meant more to send a message to those resisting alteration of the existing order--the settler colonies.

It had the desired effect, too. Federation in central Africa was already dying, and the anger of white settlers in Southern Rhodesia eventually put the Rhodesia Front in office and directly led to the UDI in 1965 (which includes the telling language that they repudiate any agreements the British made with nationalist parties and thus set off the armed struggle that ultimately gave us Mugabe). The South Africans (especially H. F. Verwoerd) had a variety of, well, interesting responses to Macmillan (and you can hear both Macmillan's speech in Cape Town and the SA Prime Minister's response as broadcast there if you've got an hour), but none were so powerful as the Sharpeville Massacre and banning of political opposition mere months later in March 1960 which showed the ANC and PAC (and others) that the apartheid government would not negotiate and arguably set them on the path to violent action as well. Kenya, on the other hand, opted to negotiate with Kenyatta's KAU; the handful of white settlers in Tanganyika came to agreement with Julius Nyerere fairly quickly. Zambia, Gambia, Malawi all had fairly quiet paths to indepenedence but importantly retained friendly relations with the UK, which had effectively tipped the balance supporting self-determination by coming out so publicly at a time when clamor was rising for independence across the European empires. It repaired some damage to British image in the Commonwealth, it played well with the public, and it promised an end to expenditures of lives and money on the Empire at a time when WWII and Austerity were still very active memories.