On February 3, British PM Harold Macmillan gave a speech before the parliament of South Africa in Cape Town. The speech made clear that Britain intended to grant independence to many of the territories in African that were its colonies, though any specifics were lacking. The speech became famous because of this line: "The wind of change is blowing through this continent. Whether we like it or not, this growth of national consciousness is a political fact." There was also a hint--just a hint--that Britain was beginning to doubt apartheid: "As a fellow member of the Commonwealth it is our earnest desire to give South Africa our support and encouragement, but I hope you won't mind my saying frankly that there are some aspects of your policies which make it impossible for us to do this without being false to our own deep convictions about the political destinies of free men to which in our own territories we are trying to give effect."
Back in England, there was an extended backlash against the speech from the right of the Conservative Party. The speech led directly to the formation of the Conservative Monday Club pressure group.
A long extract from Macmillan's speech is here and a bit of basic analysis here.