Britain immediately went on its highest alert for terrorist attacks, raising the level issued by MI5, the domestic intelligence service, to "critical" from "severe", where it had been for several weeks.
The plan was uncovered in a joint operation by the Yard's anti-terrorist branch and the security service that lasted several months, the Metropolitan Police said.
The police said that 21 arrests had been made in London and Birmingham and that the plot involved hiding explosive devices in hand baggage.
Scotland Yard said on Thursday that security was ordered to be tightened at British airports, where departing passengers were not allowed to take hand luggage on board except articles in transparent bags.
Articles are restricted to essential items such as tickets and passports, along with medication; mothers with babies are being asked to taste bottled milk to prove it contains nothing poisonous.
The police say these restrictions could remain in place for several days.
Meanwhile, John Reid, the British home secretary, said that the alleged plot was designed to "bring down a number of aircraft through mid-flight explosions, causing a considerable loss of life".
He said that while the security services would deliver 100% effort and dedication, they could not guarantee a 100% success rate in fighting terrorism.
"We are probably in the most sustained period of severe threat since the end of world war two," Reid said in a speech to the Demos think-tank.
He called for all parts of society to band together in a common effort, in his view the only way to assure Britain's common security.
"Our security forces and the apparatus of the state provide a very necessary condition for defeating terrorism but can never be sufficient to do it on their own."
He warned of "insecurity in the heart of our communities".
Meanwhile the US has raised its security alert level for flights from the UK.