Thomas Cook holidaymakers and crew are free to leave Cuba, according to the Civil Aviation Authority.
Repatriation flights have been arranged with the aid of the British Ambassador to Cuba, it said.
Tourists had said they were prevented from leaving their hotels until they paid extra for their stay.
One holidaymaker, Sue Petrow, who was due to leave, said her hotel had told her she could be held at the airport unless she paid her bill.
Cabin crew from Thomas Cook had also said they were effectively being “held hostage” by security guards at a hotel.
But Dame Deirdre Hutton, the chair of the Civil Aviation Authority (CAA), told the BBC’s Today programme: “That has been sorted out by the ambassador overnight, and the Cuban flight is in the air on its way back, which is very good news.”
“It’s also an example of how we’re working very closely with the Foreign Office, which is great.”
“It’s very distressing for people who are finding difficulties with their accommodation, but what we’ve done is issue guarantees to the… hotels with Atol-protected British tourists,” she added.
The British Ambassador to Cuba said hotels had been instructed to allow customers to depart without paying additional charges.
Antony Stokes said on Twitter: “Very grateful for the patience of all affected in distressing circumstances.”
Sue Petrow said she and other guests had refused to pay extra charges demanded by the hotel.
Holidaymakers like Sue may have paid for their rooms and meals months in advance, but hotels would normally only receive the money from Thomas Cook several weeks after their stay.
Reports suggested there was a widespread concern in Cuba over whether the industry insurance fund Atol, which covers payments in the event of a firm failing, would foot the costs.
The fund covers bills that have been run up since Thomas Cook’s collapse on Monday morning.
However, bills run up at hotels before Thomas Cook’s collapse will not be covered. Affected hoteliers will have to apply to the liquidators for their money.
Dame Deirdre said the CAA had issued guarantees for payment to 3,000 hotels around the world, and had already started making the first payments. The CAA had 200 staff working with Thomas Cook employees, she added.
“Given how much those hotels are owed by Thomas Cook, it’s hardly surprising that they are suspicious and angry,” she said.
Thomas Cook owes hotels £338m, with one hotel in Mexico owed £2.5m, she added.
The Insolvency Service has written to local tourist boards to make sure hotels are working with the CAA on payments, Dame Hutton said.
On Monday, the CAA launched the UK’s largest peacetime repatriation operation to bring more than 150,000 people back to the UK after the collapse of the holiday firm.
So far, more than 95% of people have been brought back on their original day of departure, the CAA said.
On Tuesday, 70 flights brought back more than 14,000 passengers, it said. There are 70 flights scheduled on Wednesday, bringing back a further 16,500 people.
The flying programme will continue until 6 October with more than 1,000 flights planned.
Richard Moriarty, chief executive of the CAA, said: “I would like those remaining on holiday to enjoy the rest of their stay because we aim to also fly you home on the day when you were originally booked to fly with Thomas Cook, or very shortly thereafter.
“This remains a highly complex operation and I would like to thank holidaymakers for their patience as some inconvenience and disruption is likely.”
How are customers protected?
If you are on a package holiday, you are covered by the Atol scheme.
- The scheme will pay for your accommodation abroad, although you may have to move to a different hotel or apartment
- Atol will also pay to have you brought home if the airline is no longer operating
- If you have a holiday booked in the future, you will also be refunded by the scheme
- If you have booked a flight-only deal, you will need to apply to your travel insurance company or credit card and debit card provider to seek a refund
The CAA has set up a dedicated website to keep Thomas Cook customers updated with the latest advice and news.
It is running a call centre and Twitter feed with open direct messages to respond to holidaymakers 24 hours a day, seven days a week.
The call centre can be reached on 0300-303-2800 inside the UK and +44 1753-330330 from abroad.