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.
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But Deirdre Hutton, the chair of the Civil Aviation Authority, 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.
Antony Stokes said on Twitter: “Very grateful for patience of all affected in distressing circumstances.”
In a separate tweet, Mr Stokes said additional flights were leaving on Wednesday and Thursday.
Sue Petrow said her hotel had said Atol was not recognised in Cuba, but she and other holidaymakers had refused to pay.
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 widespread concern in Cuba over whether the industry insurance fund Atol, which covers payments in the event of a firm failing, was recognised in the country.
The fund covers bills for rooms and food 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.
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
What are your rights? Read more here.
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.