Nor did the British and South African governments. Williams' parents in Southeast London were also opposed.
The couple defied them all, and married in London. But there was a diplomatic outcry, and headlines around the world deplored the union. South Africa's apartheid government wanted the marriage annulled, because a mixed-race union made a mockery of their own race laws.
Added to all that, diamonds had been found in Bechuanaland and certain elements were desperate to keep the information from Khama.
The Foreign Office used devious means to force him into exile, and the British Government was involved in all manner of shenanigans designed to prevent the pair from returning to Bechuanaland.
Lloyd Webber said he first became interested in the story when he read an obituary for Williams, who died in 2002. That interest was rekindled when he saw a piece on a film about the couple called A United Kingdom.
It stars David Oyelowo and Rosamund Pike and is due to be released this year.
"It's such a fascinating story, and they went through the most awful times," Lloyd Webber said.
"But love ruled. And they loved music! They liked the Ink Spots. There's a lot to explore, musically.