Speaking at the Royal United Services Institute last week, Dearlove, who headed MI6 from 1999 to 2004, emphasised the significance of Prince Bandar's words, saying that they constituted "a chilling comment that I remember very well indeed".
He does not doubt that substantial and sustained funding from private donors in Saudi Arabia and Qatar, to which the authorities may have turned a blind eye, has played a central role in the Isis surge into Sunni areas of Iraq.
But the change is very recent, still ambivalent and may be too late: it was only last week that a Saudi prince said he would no longer fund a satellite television station notorious for its anti-Shia bias based in Egypt.
The problem for the Saudis is that their attempts since Bandar lost his job to create an anti-Maliki and anti-Assad Sunni constituency which is simultaneously against al-Qa'ida and its clones have failed.
The West may have to pay a price for its alliance with Saudi Arabia and the Gulf monarchies, which have always found Sunni jihadism more attractive than democracy.
A striking example of double standards by the western powers was the Saudi-backed suppression of peaceful democratic protests by the Shia majority in Bahrain in March 2011.
Saudi sympathy for anti-Shia "militancy" is identified in leaked US official documents.
The then US Secretary of State Hillary Clinton wrote in December 2009 in a cable released by Wikileaks that "Saudi Arabia remains a critical financial support base for al-Qa'ida, the Taliban, Le T [Lashkar-e-Taiba in Pakistan] and other terrorist groups." She said that, in so far as Saudi Arabia did act against al-Qa'ida, it was as a domestic threat and not because of its activities abroad.
This policy may now be changing with the dismissal of Prince Bandar as head of intelligence this year.
First, they are convinced that there "can be no legitimate or admissible challenge to the Islamic purity of their Wahhabi credentials as guardians of Islam's holiest shrines".
But, perhaps more significantly given the deepening Sunni-Shia confrontation, the Saudi belief that they possess a monopoly of Islamic truth leads them to be "deeply attracted towards any militancy which can effectively challenge Shia-dom".