We've never had she so good.

Supermac probably still resigns quite soon. Without the scandal, there could be a more orderly hand over to his successor (Butler misses out as in OTL). Consequently Douglas-Home is able to win the 1964 election though with a razor thin majority.
 
I don't think the discovery of the Profumo scandal made the difference between Labour winning and losing the 1964 election.

Profumo does not resign as Secretary of State for War in MacMillan's government. Douglas-Home appoints him to the cabinet. He is also in Heath's cabinet. Although a "wet", Thatcher appoints him to her cabinet when she becomes Prime Minister in 1979. He resigns in 1981. He does not contest the 1983 election and is made Baron Profumo of Stratford-on-Avon (his constituency).
 
But the election of 1964 was a very close thing. So I think its still possible, that the lack of the Profumo-scandal would lead to a Tory-victory.
 
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