The involved Argonaut, G-ALHK, had been sold to Danish holiday/charter carrier Flying Enterprise in 1961. When they went under in 1965 there was no further market for it, and it was broken up at Copenhagen I believe.
The Argonaut had been chartered from BOAC for an extended Royal trip to Australia etc over some weeks, the first leg of which was to East Africa. It was stood down at Entebbe when the news came through, and one can only imagine the efforts required to arrange the flight to London. I believe it had a single crew who were to accompany it throughout the leisurely trip.
The DC-3 VP-KHK which performed the initial link flight to Entebbe was sold a couple of years later to the French Air Force, for whom it performed long term. In 1969 it was sent to Scottish Aviation at Prestwick, one of the few remaining DC3 MROs in Europe by then, and while standing on the ramp it was overturned in a severe gale, and damaged beyond repair.
There was a more detailed discussion by several of us here a few months ago, on the actual anniversary of the accession, including a picture of the damaged Dakota at Prestwick :
Death of King George VI and accession of HM Queen Elizabeth II - PPRuNe Forums