Tanvir Hussain, Abdulla Ahmed Ali and Assad Sarwar were found guilty
Counter-terrorism officials are said to be "dismayed" by the outcome of a trial in which eight men were accused of a plot to blow up transatlantic planes.
Three men were convicted of conspiracy to murder but the jury did not convict any defendant of targeting aircraft. One man was cleared of all charges.
The BBC's Frank Gardner said there had been "astonishment" in Whitehall as the evidence was considered to be strong.
Prosecutors have until the end of the month to consider a retrial of the men.
Abdulla Ahmed Ali, Assad Sarwar and Tanvir Hussain were convicted of conspiracy to murder but a jury was unable to reach verdicts on the other charge.
The court was also unable to reach any verdicts on four other men.
The men had been accused of plotting to bring down transatlantic airliners with home-made liquid explosives disguised as soft drinks.
Sweeping airport restrictions on liquids in hand luggage were brought in following the arrests in August 2006.
Limits remain
Despite the verdicts, the government said the case had proven it was possible to "create liquid bombs from domestic items" and that limits would remain in place.
A statement from the Department for Transport said: "Aircraft could be vulnerable to such devices so we are right to continue to require restrictions for liquids carried as hand luggage."
Efforts to develop new detection methods which would allow the restrictions to be eased would continue, it added.
Frank Gardner, the BBC's security correspondent, said counter-terrorism officials had thought it was an open-and-shut case, with the strongest evidence yet in a British terror trial.
Police and prosecutors expected the jury to accept the alleged links between the accused, al-Qaeda and a fleet of transatlantic airliners, he said.
And jurors were unable to reach verdicts on those charges or conspiracy to murder charges against Ibrahim Savant, 27, of Stoke Newington, Umar Islam, 30, of Plaistow, and Waheed Zaman, 24, and Arafat Waheed Khan, 27, both of Walthamstow, all London.
Mohammad Gulzar, 27, of Barking, east London, was found not guilty on both counts.
Home Secretary Jacqui Smith said the police and security services had saved "countless" lives by disrupting the group.
Professor Michael Clarke, the director of the Royal United Services Institute, told BBC Radio 4's Today programme that the pressure for early arrests may have come from President Bush - even though he had reportedly been advised to wait by the then prime minister, Tony Blair.
Prof Clarke said the case reflected the different approaches of the British and the Americans.
"The United States say they are in a 'war against terror' and all they want to do is smash any conspiracies.
"What we're concerned with is a criminal justice approach. What we want is evidence that would be admissible in court because for us this is an issue of criminality.
"For the British, the evidence will never be better than the night before the plot is sprung. For the Americans when you see a plot you break it."
Recorded videos
The court heard prosecutors allege that the eight men were planning to carry liquid explosives on to planes at Heathrow, knowing the devices would evade airport security checks.
Police said the plot had been inspired by al-Qaeda in Pakistan - and the August 2006 arrests caused chaos at airports throughout the country.
But in their defence, the seven men, who had recorded videos denouncing Western foreign policy, said they had only planned to cause a political spectacle and not to kill anyone.
Ali, the ringleader, of Walthamstow, east London, created home-made liquid explosives in a flat which prosecutors said were designed to evade airport security.
Jacqui Smith welcomes the verdict
He and five of the others - Mr Savant, Mr Islam, Mr Zaman, Hussain and Mr Khan - had recorded what the prosecution alleged were "martyrdom videos" denouncing the West and urging Muslims to fight.
Prosecutors said the bombers would then have completed and detonated the devices during their flights once all the targeted planes had taken off.
The plot came to light after the largest ever surveillance operation involving officers from both MI5, the Metropolitan Police and other forces around the country.
Ali, Sarwar and Hussain, along with Mr Savant, Mr Islam, Mr Khan, and Mr Zaman, also admitted conspiring to cause a public nuisance by making videos threatening bombings.
One-Minute World News 
E-mail this to a friend 
Printable version 
BBC News
Bookmark with:
What are these?