The newspaper said the plot to target the House of Commons, or lower house, was prepared last year and had been discovered in coded e-mails on computers seized from terror suspects in Britain and Pakistan.
"Police and (domestic intelligence agency) MI5 then identified an Al-Qaeda cell that had carried out extensive research and video-recorded reconnaissance missions in preparation for the attack," it said.
The paper based its report on an internal police document it said it had obtained detailing a meeting of senior police officers held last month.
It quoted an unnamed senior police officer as saying that the plot involved a gas or chemical "dirty bomb" attack against parliament.
"The House of Commons was one of their targets as well as the Tube (Underground subway network)," he reportedly said.
"They were planning to use chemicals, a dirty bomb and sarin gas. They looked at all sorts of ways of delivering it."
The report said police had decoded the e-mails with the help of an informant from al-Qaida.
On Saturday, London's Metropolitan Police said it had reviewed the use of deadly force against suspected terrorists after the killing of an innocent man but made only minor changes.
"There has been a review. The police have reviewed the strategy and we have made one or two small changes, but the operation remains essentially the same," a police spokeswoman said on Saturday.
Jean Charles de Menezes was killed
by British police on 22 July
She declined to discuss details of the changes in Operation Kratos, the force's name for what British media call a shoot-to-kill policy.
The review comes after the 22 July killing of a Brazilian man, Jean Charles de Menezes, 27, who was wrongly suspected of being a bomber.
A newspaper report also said that the official level of threat to Britain from terrorist attack had been lowered for the first time since the 7 July bombings, which killed 52 commuters.
The Sunday Telegraph reported that intelligence officials had reduced the threat level from the highest rating of «critical» down to «severe general» because there was no specific intelligence of an imminent repeat of attacks.
Police on Saturday denied a report that they had offered $1 million in compensation to the dead Brazilian man's family.
"The only discussions we have had so far with the family of Jean Charles de Menezes have been about initial expenses and we strongly refute any suggestion that a figure anywhere in the region of one million dollars has been offered as compensation," the force said in a statement.
A report in Saturday's editions of The Daily Mail said a senior officer had made an initial offer of compensation during a visit to Brazil two weeks ago.