Police made the arrests on Thursday after raids in London, southeast England and Birmingham.
Paul Stephenson, the deputy commissioner of London's police, said: "We are confident we have disrupted a plan by terrorists to cause untold death and destruction.
"Put simply, this was intended to be mass murder on an unimaginable scale."
Britain and the US stepped up security, causing severe delays at airports following the announcement of the reported plot, which a police source said was believed to involve concealing a "liquid chemical" device in hand luggage.
British police sources did not rule out US suggestions of a link to al Qaeda, but played down direct involvement by the global group.
Police sources said some of those arrested were British Muslims.
John Reid, the British home secretary, told a press conference that the alleged plot had been designed to "bring down a number of aircraft through mid-flight explosions".
He said that British police were confident "the main players have been accounted for".
"Put simply, this was intended to be mass murder on an unimaginable scale"
Paul Stephenson, London police
Police said the plan was uncovered in a joint operation by Scotland Yard's anti-terrorism branch and the security service that lasted several months.
London's Heathrow airport, the busiest in Europe, closed to most European flights following the alert, officials said.
Nicolas Sarkozy, the French Interior Minister, said the suspects "appear to be of Pakistani origin" and said Paris had been in close contact with British authorities.
A police official said British authorities had been working closely with the South Asian community.
Britain and the US immediately went on the highest level of alert for attacks. Britain raised the level issued by MI5, the domestic intelligence service, to "critical" from "severe", where it had been for several weeks.
US authorities issued a "Red" terrorism alert for the first time.
Michael Chertoff, the head of homeland security, said the plot involved using liquid explosives and detonating devices disguised as beverages, electronic devices, or other common objects.
He said: "This operation is in some respects suggestive of an al Qaeda plot, but because the investigation is still underway, we cannot yet form a definitive conclusion."
Chertoff said the plotters had been very close to carrying out the attacks when British police moved in.
"They had accumulated and assembled the capabilities that they needed and they were in the final stages of planning before execution."
Tony Snow, the White House spokesman, said Thursday's arrests were the result of extensive investigations and that George Bush, the US president, and Tony Blair, the British prime minister, had discussed the plot "in recent days".
Departure halls in Britain were jammed with people waiting as airlines cancelled flights and trying to sort out their bags as hand luggage and liquids were banned from flights and passengers with babies were made to publicly taste their food.