A notebook was reportedly found in a house in the southern Afghan city of Kandahar from which followers of Osama Bin Laden "are believed to have fled in a hurry".
The notebook is said to have contained plans to detonate a 480kg remote control device "to be left in a van parked preferably in Moorgate, in the City of London".
The planned attack is reported in both The Observer newspaper in London and the Expresso newspaper, based in Lisbon in Portugal.
Expresso said neither the author of the notes nor the time they were written were known, nor was it known whether the document was "simply a hypothetical exercise".
But The Observer says the author of the notebook may have been a British fundamentalist.
It said it was not yet known whether the author stayed to fight and die with the al-Qaeda network or has already left for Britain.
Expresso said the only clue about a timetable for the operation was the phrase "primary strategy - 1-2 weeks".
The alleged plans to attack London were written in English, with Arabic sentences interspersed, "practically without errors and with uniform handwriting, thus suggesting it was written by one person only", the paper said.
Inventory
The notebook contained a detailed inventory of equipment for assembling the device: 12 40kg boxes, each with three detonators.
The plan was divided into the following stages: "1- electrical/electronic circuit; 2 - assembly inside the van; 3 - carry out several tests".
Further on, Expresso said, the notebook pointed to a possible travel itinerary for those involved in the operation.
It contained the notes "never work alone"; "Waterloo train"; "show passport"; "not bound for Dover". A few pages on came a reference to Moorgate.
Further advice was written down for those involved, such as "make money, travel, marry, talk about money, go out in the evenings, buy PC - Internet" and "sell all the books".
Other advice underlined read: "Be confident; do not panic; do not be afraid; be moderate" and "learn to listen; to obey; to be able to work without full knowledge; to never discuss (or answer without being asked)".
It ended with a detailed explanation and drawings on how to assemble the detonators, how to produce the bomb and test its circuits.
The "rules of detonation" concluded with an unequivocal "get away as soon as possible".
Lessons
Expresso said the document was just one of many items left in "what might have been a school or a base used by soldiers of different nationalities".
The building was used for various courses and lectures in different languages, on the use of firearms, explosives and other ammunition, on ambush techniques, topography and cryptology, the Arabic language, maths, and elementary physics and chemistry.
Remote-controlled van bombs were used in the attacks on the US embassies in Kenya and Tanzania in 1998 which killed more than 200 people, the vast majority Kenyans. The bombings were blamed on al-Qaeda.