* Head of air traffic control provider says issue fixed

* To present report into issue on Monday

* IATA estimates $126 million cost to airlines

LONDON, Aug 30 (Reuters) - The air traffic control glitch which caused thousands of flight cancellations and delays into and out of Britain has been fixed and will not be repeated, the head of NATS, the country's air traffic control provider, said on Wednesday.

Thousands of Britons remain stranded abroad after 1,500 flights were cancelled on Monday and disruption to schedules persisted into Tuesday. The peak holiday period means those affected are not being offered alternative flights for days.

Martin Rolfe, the CEO of NATS, said the technical problem was caused by a flight plan which was "not sufficiently standard". He said the issue had been fixed.

"We've worked incredibly hard since we restored the service back on Monday to make sure that this type of event can't happen again," he told the BBC.

Ryanair criticised NATS on Tuesday for not having a back-up system. With crews and planes in the wrong places, airlines are now scrambling to get passengers home, a process with which NATS is involved.

EasyJet said it was adding five extra flights from holiday hotspots in Portugal and Spain later this week to fly people home.

NATS will present a report on what went wrong to the transport minister on Monday, Rolfe said.

Once the immediate headache of repatriation is resolved, airlines will be focused on the bill.

The cost to carriers will be substantial said Willie Walsh, the former chief executive of British Airways who now heads up global airlines body IATA.

"I would imagine that at an industry level, we've been getting close to 100 million pounds ($126 million) of additional costs that airlines have encountered as a result," Walsh told BBC radio, adding that authorities needed to look at who bears that cost.

"It's very unfair because the air traffic control system which was at the heart of this failure doesn't pay a single penny."

Under current rules, passengers can claim back costs from airlines for accommodation booked as a result of a cancelled flight, but they will not be entitled to compensation if the disruption is put down to "extraordinary circumstances".

NATS is a public-private partnership which is partially owned by airlines including British Airways and easyJet and pension funds and partially owned by the government. (Editing by Kate Holton and Janet Lawrence)