First plane to land at Heathrow since last Thursday
Flights have landed at a number of UK airports for the first time in six days following the lifting of restrictions caused by a volcanic ash cloud.
The Civil Aviation Authority allowed a phased reopening of airspace after a reassessment of the risk to aircraft.
It said its safety tests showed that plane engines had "increased tolerance levels in low ash density areas".
BAA, which operates many of the UK's airports, said people should contact their airlines before travelling.
"Not all flights will operate during the early period of opening, and we will do everything we can to support airlines and get people moving," a spokesman said.
Some restrictions will remain on flights in UK airspace, but they will be much less stringent than before.
Dame Deirdre Hutton, of the Civil Aviation Authority (CAA), said there had been detailed consultation with experts to reassess the tolerance of planes to the ash cloud.
The CAA said it was a "situation without precedent" and that decisions had been made based on "thorough gathering of data and analysis".
"The major barrier to resuming flight has been understanding tolerance levels of aircraft to ash," the CAA said.
"Manufacturers have now agreed increased tolerance levels in low ash density areas."
Transport Secretary Lord Adonis, who made the initial announcement, denied the decision to reopen airspace was the result of pressure from the airline industry.
He told BBC Two's Newsnight programme: "The issue at stake here has been the assessment of the safety authorities as to what is the safe way in which planes can fly when there is a presence of ash.
"The fact which has changed in the last week is we have had a volcanic eruption and having to assess safe levels of ash content in the atmosphere within which planes can fly has been an urgent issue which the safety authorities have had to deal with."
Prime Minister Gordon Brown said: "This solution has been reached as a result of the close working between the government, the Civil Aviation Authority, airlines and the manufacturers, and will allow the thousands of UK citizens stranded abroad to return home to their families.
Dame Deirdre Hutton, Civil Aviation Authority: "We're issuing new guidance"
"We will of course continue to monitor the situation closely; as we have said throughout safety is our primary concern," he added.
But shadow transport secretary Theresa Villiers said Labour's "misjudgement and mismanagement" had "badly let down" the travelling public and urged the Prime Minister to immediately announce a full inquiry into the "fiasco".
She added: "Six days into the crisis, we're suddenly told that there are actually levels of ash which are compatible with safe flying. The question angry passengers and airlines are already asking is why the government hadn't worked this out before the crisis occurred."
After the lifting of the restrictions, the first British Airways flight to touch down from Heathrow was a service already in the air from Vancouver, which landed shortly before 2200 BST.
The airline's chief executive Willie Walsh said he was pleased with the decision, but said it would take weeks to get back to normal levels of operation.
"We're now at British Airways going to start the difficult task of getting our stranded customers back home but I think this is an airlift that is unprecedented but we will make every effort to get our people back home."
He said "lessons can be learned" and added: "There will be plenty of time for a post-mortem of what has happened over the last few days."
Everyone felt that if the pilot was happy to fly then we were happy to get on
He said parts of the UK airspace could have been opened several days ago. "My personal belief is that we could have safely continued operating for a period of time. I think there were occasions when the decision to close airspace could have been justified."
EasyJet said it planned to resume "some services across the UK and continental Europe from tomorrow morning," but added that the level of disruption meant it would be several days before the schedule returned to normal.
Flights have been grounded across the UK and much of Europe since Thursday following the eruption of Icelandic volcano Eyjafjallajokull.
The eruption sent vast amounts of ash into the atmosphere which poses a threat to aircraft jet engines.
Despite the lifting of the ban, it will be some time before flights return to normal.
Flight restrictions had already been eased across much of Europe earlier in the day but it was thought likely that it would be a few days before regular flight schedules would return.
Some flights have left Paris, Amsterdam and Frankfurt, but airspace in Germany and Ireland remains restricted.
As tens of thousands of Britons prepare to return home, the UK Border Agency warned people to expect long queues at passport as staff attempt to process large numbers of returning travellers.
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