Dame Deirdre Hutton told Sky News that 12,000 passengers had been brought home on Monday on the first day of the operation as the airline collapsed into administration.
A further 12,000 were expected to come back to the UK on Tuesday, which will leave 86,000 still to return.
The collapse of Britain’s fifth biggest airline on Monday morning left 110,000 holidaymakers who had planned to return on Monarch flights potentially stranded abroad.
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But the CAA has launched an operation to bring all of them home, including some who were not covered by the industry’s ATOL (Air Travel Organiser’s Licence) guarantee scheme – reportedly at a cost of up to £60m to the Government.
It is the UK’s biggest peacetime repatriation , according to the Government.
Meanwhile 750,000 people with future bookings who were yet to travel have had their trips cancelled – unless they are able to find an alternative.
Many have complained of having to pay much more for other flights and that plans including honeymoons and weddings have been jeopardised.
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Monarch’s collapse also saw 1,858 of around 2,100 people employed across its airline and tour operation made redundant.
Dame Deirdre said day one of the operation to bring customers home had gone as well as we could have hoped and the second day had started well .
However, she cautioned that there may be bumps on the way .
The programme saw 61 flights on Monday and 58 planned for Tuesday, chartered by the CAA.
No Monarch planes were used as they were leased from other companies and not owned by the collapsed airline.
We had to beg planes from all around the world to bring everybody back, Dame Deirdre said.
She advised customers to check a dedicated website for details and said, that if they could not find these, they should arrive at the airport three hours in advance of the flight they had been scheduled to take.
Many are in sunshine destinations such as the Costa del Sol, the Algarve and the Canary Islands.
Monarch’s administrators, KPMG, said the collapse followed a sustained period losses as it faced mounting cost pressures and increasingly competitive market conditions .
Monarch, which has its headquarters at Luton Airport, is the biggest UK airline ever to cease trading.