Hassan made his claim in an interview with the BBC, and said that he had alerted Pakistan President Asif Ali Zardari to the threat.
Zardari in turn urgently contacted senior British and American officials who intervened to calm the situation.
There was no response to the claims from the British Foreign Office.
The Sun quoted a spokeswoman as saying: "We do not comment on security issues".
The revelations come after it was revealed that one of two Indians arrested in Kolkata on Saturday over the attacks is a counter-insurgency police officer who may have been on an undercover mission.
The man was arrested for buying mobile phone cards used by the gunmen in the attacks.
A senior Jammu and Kashmir police official was quoted as saying that Mukhtar Ahmed, is part of a semi-official counter-insurgency network whose members are usually drawn from among former militants.
The official says Kolkata Police, who are holding Ahmed, have been told he is "our man and its now up to them how to facilitate his release." (ANI)