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Thousands of air passengers have returned to the UK after a six-day flight ban caused by volcanic ash.Others remain stranded overseas, however, and travel companies think it may take weeks to repatriate everybody.
Despite the large backlog, London's Heathrow Airport has begun operating at 90% normal service, with other airports and airlines following its lead.
Transport Secretary Lord Adonis has said the ban was "too cautious" and some airlines want compensation.
KEY POINTS NOWUK and European airports reopen for businessMany flights still cancelled or delayedAirlines begin to repatriate stranded passengers80% of European flights due to operateFlight disruptions cost airlines $1.7bn (?1.1bn)Icelandic volcano has lost 80% of its intensityUpdated: 17:36 BST, 21 April
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He told the BBC that regulators had needed time to test the impact of the ash.
Officials from Airline Co-ordination Limited said service at Heathrow Airport should be at 100% by Thursday but that figure includes only regularly scheduled flights.
The Department of Transport has said that Heathrow, the UK's main hub, will temporarily be allowed to accept 16 extra night flights late on Wednesday.
UK airspace was opened at 2200 BST on Tuesday, and for the first time in almost a week, there have been scenes of joy at UK airports with passengers finally arriving home.
Many departures and arrivals boards at many airports remain full of cancellations, however.
Easyjet chief executive Andy Harrison said his company would be seeking £50m compensation from the government, while British Airways chief executive Willie Walsh said it would take weeks to get back to normal.
"I think this is an airlift that is unprecedented but we will make every effort to get our people back home," he said.
BAA chief operating officer Nick Cullen said the lack of passengers coming through the company's airports had led to daily losses of around £5m to £6m.
Ryanair has said it will defy EU regulations and warned customers it will only reimburse customers their airfare and no additional expenses.
More than 95,000 flights were cancelled across Europe over the past six days, with only a handful of flights taking off and landing at UK airports.
The eruption of the Icelandic volcano Eyjafjallajokull on Thursday sent vast amounts of ash into the atmosphere and posed a threat to aircraft jet engines. Scientists say the volcano is still erupting but the ash plume is shrinking, although it remains changeable.
Air traffic control body Nats said a dense concentration of volcanic ash continued to remain in an area over north west Scotland and could extend further south into Scottish airspace.
Restrictions were lifted after the Civil Aviation Authority said safety tests showed plane engines had "increased tolerance levels in low ash density areas".
It has set down new requirements for airlines such as conducting risk assessments and inspecting aircraft for ash damage before and after each flight.
Prime Minister Gordon Brown defended the time taken to reopen UK airspace, saying decisions had been based on "scientific advice".
"We would never be forgiven if we had let planes fly and there was a real danger to people's lives," he said.
Lord Adonis said the banwas lifted after a "robust safety assessment" based on observational data and test flights. He denied the decision to reopen the airspace was the result of pressure from the airline industry.
Conservative leader David Cameron called for a "rapid inquiry" into how the crisis was handled and said there had been "muddle and confusion" over the information people were given.
Liberal Democrats leader Nick Clegg, whose three sons were stranded in Spain, told Sky News a "post-mortem" of how the situation was dealt with would be needed.
In other developments:
Helicopter flights over the North Seawere cancelled after two aircraft reported being covered with volcanic ashAll flights out of Orkney and Shetlandhave been suspended because of ash density in the air Britons stuck on mainland Europe are still being advised to make their way to France's northern ports to catch a ferry across the Channel. Coaches hired by the Foreign and Commonwealth Office (FCO) have been leaving Madrid bound for northern France and more will be available. Rail lines serving Gatwick, Heathrow and Stansted airports will stay open overnight to help stranded passengers get home. Anyone concerned about the safety of a British national who is still stranded abroad can call a Foreign Office helpline on 020 7008 0000, or visit itswebsite.
Stranded Britons should contact their local embassy, high commission or consulate.
Are you due to fly today? Have you made it to your destination? Or are you still stranded? Are you an airline staff member? Send us your comments.
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