Thomas Cook will run 11 flights, including nine extra departures, to evacuate people over the next two days.
The Foreign Office has advised against all travel to the capital Banjul and against all but essential travel to the rest of the West African country.
It comes after Gambian President Yahya Jammeh refused to step down after losing a disputed election last month.
West African military forces say they are ready to enforce a transfer of power in The Gambia.
Two Thomas Cook planes returned to Manchester airport on Wednesday night, and another was due back in the early hours of Thursday.
Two additional flights were also expected to land at Gatwick.
Four additional flights, as well as a scheduled one, will land in the UK on Thursday, returning about 1,000 customers to Gatwick, Manchester and Birmingham airports.
Thomas Cook said it had brought back 1,038 customers from The Gambia on Wednesday, and by the end of Friday it expected to have brought home about 3,500 passengers on a total of 16 flights.
UK holidaymakers forced to rethink breaks
Returning holidaymakers have been speaking about the situation in the country.
Sara Wilkins, from Shropshire, said: "Last night it all got a bit too serious - all the restaurants shut down, all the shops shut down - and it got really scary.
"The local people were crying and worried about their children, and they've got no work now because there's no tourists, so I don't know how they're going to survive."
"We're just relieved to be back."
The president of the Gambia, Yahya Jemmeh, refused to step down after losing the country's election last month.
Mr Jammeh claims there has been "extraordinary" foreign interference in the election and has now missed the deadline to remove himself.
Adama Barrow, who beat him, has now been inaugurated at his country's embassy in neighbouring Senegal.
The situation has led to growing political unrest in the country.
Senegal moved troops towards the Gambian border in an effort to force Mr Jammeh to accept electoral defeat and step down.
The threat of military action is supported by Nigeria and other states in the region.
At least 26,000 Gambians have sought refuge in Senegal this week amid fears that violence could erupt.
Mr Jammeh has ruled The Gambia since taking power in a coup in 1994.
Gambia political crisis: What happens next?
Alan Harper, from Warrington, said: "We went out on a trip on Monday and the Gambian people getting on the ferry were carrying all their possessions.
"It was a real struggle to get on the ferry. Everybody was just fleeing. We thought then that something was seriously wrong.
"We went out on Wednesday night to a Chinese restaurant and they said, 'We're closing within the hour,' so we had to have our main course and get straight out.
"All the Gambian people who worked there were coming straight out because they were frightened to death. They were hurrying home."
Gambian Ebrima Jagne, a textile engineer who works in Burnley, Lancashire, arrived at Manchester airport on one of the flights, but was concerned for his wife Haddytouray and their three-month-old daughter, Ajiamina Jane, whom he is trying to get out of the country.
He said everyone in the country felt "unsafe" and "on edge... because you don't know what's going to come next".
"I cannot get my daughter out," he added. "I'm desperate. It's not easy at all when I leave my wife there and daughter."
Mark Hammans has dedicated 30 years to raising money for The Gambia.
Two years ago, the 53-year-old decided to set up his own charity, Aid to Gambia, and the team managed to raise enough cash to buy three ambulances to send to the country.
His partner, Lynn Bowcock, told the BBC: "He goes out there every year, twice a year, taking crates of supplies for schools. He lives for Gambia."
But when he set off from Nottingham on New Year's Day to drive the vehicles to the country, little did he know that he would struggle to get home.
He had booked flights back to the UK with Thomas Cook, but Ms Bowcock was told as he had not flown there with the company, they were not obliged to make sure he got a flight home.
"It is just horrible," she told the BBC. "If I called them once yesterday, I called them a dozen times. We are so stressed. I have got three children and we just want him to come home."
A Thomas Cook spokeswoman told the BBC the company was continuing to work hard to get all its UK customers home as quickly as possible.
She added: "I can confirm that we have spoken to Mr Hammans. We have apologised for any misunderstanding and made arrangements for [his] whole party to fly on Friday on the 16:00 GMT flight to Birmingham."
Other passengers described the rush at hotels to get them out.
Pensioner Sue Thrower, from Doncaster, said she had only learned of the evacuation through a woman who was talking to her mum back home, while Ralph Newton, from Nottingham, said he had only found out an hour before they had to leave.
Hilary Cox, who returned home to Kensington on Thursday morning having cut short her holiday by one day, said: "On Tuesday rumours started about tourists being told to fly back home. Our hotel reception was heaving.
"There was a lot of humour and a lot of tension. Nobody was frightened. Some people who were booked out for two or three months were refusing to go."
Arlene Robertson is still stuck in the Gambia and told BBC Radio Scotland there were few people left in her hotel and staff were not showing up for work.
"I want to stay because it's beautiful, but the atmosphere and the current situation is horrible. At least I would have liked to enjoy my holiday, but I can't stay, there's too much uncertainty and I'm concerned about my family worrying about me and about my own safety as well.
"There's two of us in the hotel and they have no milk left, they have no breakfast," she said. "Most of the staff have left as well, some have families and have gone to Senegal already."
Thomas Cook is now offering free amendments or cancellations for holidays to The Gambia up to and including 31 January.
The company has also set up a phone line for flight-only customers who are still in The Gambia and or anyone there needing help: 00 44 161 774 2966.
The first flights carrying British tourists evacuated from The Gambia have arrived back in the UK.