It was divide and rule mainly.
Then the British also tried - Sterilise and Rule.
That's how the British and Queen Victoria allegedly tried to bring the Rajasthan Royals to an end.
Read this link from TOI :
But that's ok with some people. But, what if the Royal foraged among some others than his wife and then produced some results? The British might have banked on the fact that the illegitimates won't be getting the same public backing as the legitimates.
But then would'nt the assassination of the Royal himself, have been a better plan for the British rather than lurking around the Royals bedroom and attempting family planning ?