The Civil Aviation Authority (CAA) has repatriated nearly 15,000 Thomas Cook customers following the travel company's collapse.
CAA completed 64 flights on the first day of the operation, bringing 14,700 people back to the UK.
It was estimated that more than 155,000 travellers were affected following the collapse of Thomas Cook.
The CAA say that over 95 per cent of all those due to return yesterday were repatriated.
It is expected to bring back 16,800 people on 74 flights on Tuesday.
Operation Matterhorn is expected to cost the taxpayer up to £100m - £50m less than the minimum bail out the travel company asked for.
The government said it would run a "shadow airline" for two weeks to repatriate UK tourists.
The CAA said: "With 13 days remaining and approximately 135,300 passengers still to bring back to the UK, we are working around the clock, in conjunction with the Government and the aviation industry, to deliver the flying programme after Thomas Cook ceased trading.
"On Tuesday 24 September, day two of the flying programme, we plan to operate a further 74 flights, with seats for more than 16,800 people to travel back to the UK."
Holidaymakers were being brought home amid questions over the multi-million pound sums received by the bosses of the firm prior to its collapse.
READ MORE: Thomas Cook warns it could 'run out of money' and go bust
Thomas Cook bosses' actions will face scrutiny as part of an investigation into the travel firm's collapse
Business secretary Andrea Leadsom asked the official receiver, which oversees liquidations, to look at whether bosses' actions "caused detriment to creditors or to the pension schemes".
Transport secretary Grant Shapps said on Monday that its response to the crisis was "on track so far" and "running smoothly".
Richard Moriarty, chief executive of the CAA, said the Government had asked his organisation to launch "the UK's largest ever peacetime repatriation".
Forty-five aircraft from as far away as Malaysia have been chartered to operate approximately 1,000 flights from 53 airports in 18 countries over the next fortnight.
Richard Moriarty, chief executive at the Civil Aviation Authority, said: “Following the very sad news yesterday morning that Thomas Cook had stopped trading and its aircraft were grounded, we launched at the Government's request our operation to return more than 100,000 people to the UK. A repatriation of this scale and nature is unprecedented and unfortunately there will be some inconvenience and disruption for customers. We will do everything we can to minimise this as the operation continues.
“However, I am pleased to report that on day one we brought home over 95 per cent of people who were originally due back on this day with Thomas Cook; 14,700 people in total. We want people to continue to enjoy their holiday, so we will bring them back to the UK on their original departure day, or very soon thereafter.”
On Monday evening, the Prime Minister visited staff at the British consulate in New York City, who are working to bring stranded travellers home.
He tweeted: "It's a tough time for those who have had holidays disrupted but team hard at work to support them.
READ MORE: Thomas Cook - Everything you need to know as travel firm collapses
"Thanks to all the staff who represent our country so well."
Earlier in the day, Mr Johnson questioned whether directors should pay themselves "large sums of money" as their businesses go "down the tubes".
Liquidators will now see if any money can be found within more than 25 Thomas Cookcompanies to hand back to staff and creditors.
The travel agent had about 550 high street locations across the UK, however, it leased its planes, rented its shops and acted as a broker with third-party hotels and cruise ships, meaning it has minimal assets.
Some staff on the final Thomas Cook journeys on Monday evening were informed mid-flight that they had been made redundant effective immediately.
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