Thomas Cook vacationers and crew are free to leave Cuba, according to the Civil Aviation Authority.
Domestic flights have been arranged with the help of the British ambassador to Cuba, it says.
Tourists had said that they were prevented from leaving their hotels until they paid extra for their stay.
A vacationer, Sue Petrow, who was about to leave, said her hotel had told her she could be kept at the airport unless she paid the bill.
Thomas Cook's cabin crew had also said that they were effectively "held hostage" by security guards at a hotel.
But Dame Deirdre Hutton, chairman of the Civil Aviation Authority (CAA), told the BBC's program today: "It has been sorted out by the ambassador overnight and the Cuban flight is on the way back, which is very good news. "
" It is also an example of how we work very closely with the Foreign Office, which is great. "
" It is very disturbing for people who find accommodation problems, but what we have done is to issue guarantees to … the hotels with Atol-protected British tourists, "she added.
The British ambassador to Cuba said that the hotels had been instructed to allow customers to leave without paying any additional costs.
Antony Stokes said on Twitter : "Very grateful for the patience of all concerned in troubling circumstances."
Sue Petrow said she and other guests had refused to pay any extra fees the hotel requires.
Holidaymakers like Sue may have paid for their rooms and meals months in advance, but hotels will normally only receive the money from Thomas Cook several weeks after their stay.
Reports indicated that there was widespread concern in Cuba about the industry insurance fund Atol, which covers payments in the event a company fails, would incur costs.
The fund covers bills that have been run up since Thomas Cook's collapse on Mond ay morning.
However, bills will run in hotels before Thomas Cook's collapse will not be covered. Affected hotel owners must seek liquidators for their money.
Dame Deirdre said that the CAA had provided guarantees for payment to 3,000 hotels around the world and had already begun making the first payments. The Civil Aviation Authority had 200 employees working with Thomas Cook employees, she added.
"Given how much these hotels are due to Thomas Cook, it is hardly surprising that they are suspicious and angry," she said.
Thomas Cook owes £ 338 million, with one hotel in Mexico owing £ 2.5 million, she added.
Insolvency Service has written to local tourist boards to ensure hotels work with CAA on payments, Dame Hutton said.
On Monday, CAA launched the UK's largest peace operation for peacekeeping bringing more than 150,000 people back to the UK following the breakdown of the holiday company.
So far, more than 95% of people have been brought back on their original day of departure, CAA said.
On Tuesday, 70 flights brought back more than 14,000 passengers, it says. There are 70 flights scheduled on Wednesday, bringing another 16,500 people back.
The flight program will continue until October 6 with more than 1,000 flights scheduled.
Richard Moriarty, CEO of CAA, said: "I would like those who are on vacation to enjoy the rest of their stay because we aim to fly you home the day you were originally booked to fly with Thomas Cook, or very shortly thereafter.
"This is still a very complex operation and I would like to thank the holidaymakers for their patience as there are likely to be some disadvantages and disruptions. "
How are customers protected?
If you are on holiday, you are covered by the Atol scheme.
- The scheme pays for accommodation abroad, although you may have to move to another hotel or apartment  Atol also pays to take you home if the airline is no longer in operation
- If you have booked a holiday in the future, you will a Then you will be refunded the scheme
- If you have booked an airline ticket, you must you seek your travel insurance company or credit and debit card provider for a refund
What are your rights Read more here
The Civil Aviation Authority has set up its own website to keep Thomas Cook customers up to date with the latest advice and news.
It operates a call center and Twitter feed with open instant messages to respond to vacationers 24 hours a day, seven days a week.
The telephone center can be reached at 0300-303-2800 in the United Kingdom and +44 1753- 330330 from abroad.
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