The policy of 'No Independence Before Majority Rule' came out of the September 1966 meeting of the Commonwealth of Nations. At that meeting, Commonwealth members from the Caribbean, Asia and Africa (minus Southern Rhodesia) caucused together and proposed that the Commonwealth position should be No Independence Before Majority Rule. East African leaders like Milton Obote, Jomo Kenyatta and Kenneth Kaunda were particularly prominent in pushing this position, as they had already met in Dar es Salaam in Tanzania to articulate a unified strategy prior to the opening of the Commonwealth meeting.

On the other hand the UK, Australia and New Zealand formed a bloc resistant to NIBMAR. British PM Harold Wilson had previously been engaged in negotiations with Ian Smith that established a formula for independence, and was resentful at being forced to backtrack from those negotiations. Wilson proposed to the commonwealth a phased plan where UK would engage in another round of negotiations with Smith, and if Smith remained intransigent on points of contention, UK would end negotiations and then support NIBMAR.

In between these two blocks was the government of Canada which sought to build a consensus between the two factions, and Harold Wilson gave Canadian PM Lester Pearson the task of writing a compromise draft communique that would present a consensus Commonwealth position on the Rhodesia issue. Pearson's compromise draft included NIBMAR as "the demand of a majority of the Commonwealth". Pearson's draft was ultimately adopted by the meeting.

So, NIBMAR was not a British attempt to maintain control over Rhodesia, it was a position articulated by African heads of state and forced on UK by diplomatic pressure.

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Source

UDI: The international relations of the Rhodesian Rebellion by Robert Goode, pp 170-177