It is thought the plan was to detonate explosive devices smuggled in hand luggage on to as many as 10 aircraft.
Police are searching premises after 21 people were arrested. Home Secretary John Reid said they believed the "main players" were accounted for.
High security is causing delays at all UK airports.
BBC security correspondent Gordon Corera said the plot was thought to have involved a series of "waves" of simultaneous attacks, targeting three planes each time.
He also said the plan "revolved around liquids of some kind".
"Officials say the explosives would have been sophisticated and extremely effective," our correspondent said.
Meanwhile, Heathrow Airport has been closed to all incoming short-haul flights with long-haul services seriously delayed. Several outbound services have also been cancelled.
The airport is crammed with thousands of passengers, while at Stansted more than 2,000 people are queuing to pass through customs.
Passengers are not allowed to take any hand luggage on to any flights in the UK, the department said.
Only the barest essentials - including passports and wallets - will be allowed to be carried on board in transparent plastic bags.
"We hope that these measures, which are being kept under review by the government, will need to be in place for a limited period only," the statement said.
I'm glad the plot was foiled, but it still must be awful to be in Heathrow right now .
Edited by Lyric Z D, 10 August 2006 - 08:58 AM.