This would probably have been in the 50's, so of course, it wasn't this particular Aga Khan.
The current Aga Khan IV is the son of II and II's first wife, Joan Yarde-Fuller.
The Aga Khan is half-English and his heir, the presumptive Aga Khan V, is his son by his first wife Sally Croker-Poole.
The Aga Khan V is three-quarters English and has been raised in the UK from birth.
However, I was wrong.
I had forgotten that the current Aga Khan is the grandson of the Aga Khan III, because the Aga Khan's father died in 1960 at the age of 49.
His father, Prince Ali Khan, would have been the Aga Khan IV, but the Aga Khan III died in 1957 and Prince Ali Khan - the heir presumptive - was already unwell and so he abdicated in favor of his 21 year old son, the current Aga Khan IV.
Prince Ali Khan was half Persian and half Italian.
His son, the current Aga Khan, is half English, a quarter Italian and a quarter Persian.
His son, the presumptive Aga Khan V, is three quarters English, one eighth Italian and only one-eighth Persian.
However, the presumptive Aga Khan V is almost 40 and has not yet married or produced an heir.
His younger brother - a naturalized American citizen - is marrying an American woman of Mayflower pedigree named Kristin White.
If they have a son and his brother never does, the Aga Khan VI will be only 1/16th Persian.
I think it was ALI Khan and yes, they did marry and (I believe) have a daughter.