Wasn't it little less direct than this? I thought that the US/UK installed the Shah to replace the democratic Iranian government. He was overthrown by the revolution in 1979 and it was following this revolution (which included elements of secularists as well as islamists) that the ayatollahs took control? The US/UK never backed the ayatollahs and started supporting Saddam in the Iran/Iraq war.

I.e. standard western fiddling about going catastrophically wrong for everyone.