Under EU regulations, if a flight is cancelled then those passengers flying on European carriers in or out of the EU have the right to a refund or to be re-routed.
If passengers choose to be re-booked by their airline, the law require carriers to cover passengers' reasonable expenses.
Earlier, budget airline Ryanair said reimbursement would be limited to the original air fare paid by each passenger.
However it later issued a statement saying it would comply with the EU rules and would refund passengers for "reasonably-receipted expenses".
Ryanair boss Michael O'Leary told the BBC passengers would not receive extra compensation for the inconvenience and the airline would seek to recover its costs - up to 40m euros (£35m) - from the EU "which closed the airspace".
Mr O'Leary also said he would continue to lobby for a change to the "grossly unfair" rules.
The EC have indicated they will compensate airlines and British holiday companies in the same way that the American government compensated airlines in America after 9/11
Sir Richard Branson
"They're not designed for European governments closing the entire European airspace for seven days," he said. "If governments close airspace, the governments should reimburse passengers, not the airlines".
Transport Secretary Lord Adonis welcomed the change of heart, saying the government and the Civil Aviation Authority had told Ryanair in the "strongest terms" that the airline could not avoid its obligations.
Easyjet said the flight ban had cost it £50m, including paying for 15,000 hotel rooms.
Oliver Aust from the airline told the BBC's Radio 4 Today programme it would compensate passengers but said that the law was "unfair".
"We accept it is in the legislation but the legislation is not fit for purpose - it was drafted to deal with overbooking, it was never meant to make airlines the insurer of last resort in a case of natural disaster," he said.
Ryanair 'will refund some expenses'
Some flight-only travellers with Tui - which owns Thomson - whose original flights were cancelled are also being told they would have to pay the difference if an alternative flight is more expensive.
But the official airline watchdog in the UK, the Air Transport Users Council, said passengers should not be asked to pay more money.
Many airlines are seeking financial help from the UK government or European authorities.
Sir Richard Branson, who owns Virgin Atlantic, told the BBC he would expect compensation.
"The EC have indicated they will compensate airlines and British holiday companies in the same way that the American government compensated airlines in America after 9/11," he said.
He also said he did not blame the UK government for the blanket ban as it was the "safe option" but lessons would be learned and it would probably never happen again.
Chris Platt, from Sheffield
We're currently stranded in Bangkok with very little information available from either airline or embassy. There are lots of conflicting rumours circulating - we hear from the UK that there are extra slots at Heathrow yet our airline doesn't know anything about this.
We've had a heated discussion with them as we could be stuck here a further three to four weeks unless they put on some extra flights.
We're in a party of 18 with one injured person who is being medically transferred on Friday night, without his wife or children. One of our party is 22 weeks pregnant - she's been given a return date four weeks from today but by then she won't be allowed to fly. We just feel like we have been forgotten.
All our expenses are being funded from our own pockets and the political protests that are going on around us make the atmosphere feel very tense. We are desperate to get back.
Lord Adonis told the BBC the flight ban had perhaps been "too cautious" but that regulators had needed time to test the impact of the ash on aircrafts.
The Ministry of Defence said that RAF training flights on Typhoons based at RAF Coningsby in Lincolnshire have been suspended, after checks on one aircraft found ash deposits in one of its engines.
Civil Aviation Authority chief executive Andrew Haines said he "made no apologies" for the length of the airspace ban, and that any independent inquiry would back his position.
More than 95,000 flights were cancelled across Europe in the past week, with only a handful of flights taking off and landing at UK airports.
The eruption of the Icelandic volcano Eyjafjallajokull on 15 April sent vast amounts of ash into the atmosphere which can be dangerous for aircraft jet engines.
The blanket ban was lifted on Tuesday night and efforts to get tens of thousands of stranded Britons home have stepped up, with airlines, trains, ferries and coaches providing extra capacity.
British Airways was running a full service at Gatwick Airport and all its long-haul flights at Heathrow on Thursday.
But it had to axe a number of short-haul flights at Heathrow and warned disruption to services would continue into the weekend.
In other developments:
• About 2,200 British tourists stranded in Spain
are returning home on board a new luxury cruise ship
in what is thought to be one of the largest peacetime repatriations to the UK. The £500m Celebrity Eclipse left Bilbao on Thursday and is expected to dock in Southampton on Friday evening
• For Britons who are trying to cross the Channel, ferry company
is advising passengers to head for the ports of Dieppe and Le Havre, where they have foot passenger capacity on Thursday and over the next day
• Many airports around the UK are returning to business as usual. UK air traffic control body Nats said a volume of airline traffic "approaching 90%" was expected from 0700 BST
• Easyjet says it has two extra planes in the air and there is now a standby facility for its passengers still stranded abroad
• BMI is flying its full international schedule on Thursday and is also operating additional flights to and from key Middle East destinations to help repatriate stranded customers. The airline says the majority of its UK and Ireland flight programme will also operate on Thursday
• Heathrow Airport was granted permission for more night landings on Wednesday
• Victoria, Paddington and Liverpool Street rail stations will remain open all night on Thursday and for the next 48 hours, as will Gatwick Airport station in West Sussex. Rail lines serving Heathrow, Gatwick and Stansted airports will also operate through the night and extra services will run into the early hours to serve the main ferry ports, including Dover. Engineering work on the main London to Scotland routes - the east and west coast main lines - has been cancelled to enable more direct services to run
Coach Hire Connections
, a subsidiary of transport giant National Express, has sent more than 250 coaches to the Continent to bring back more than 10,000 passengers
• European air traffic agency Eurocontrol said almost all European airspace is available, with a few exceptions in parts of southern Finland, northern Scotland and western Sweden
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