Olympic Holidays commercial director Photis Lambrianides admitted the decision to discount July and August holidays in early June was unusual, but he said the cuts had been prompted by a unique set of circumstances.

"Hoteliers and operators are working together to encourage the family market to commit to the Greek islands," he said.

As an example of the discounts available, Olympic has knocked £688 off a seven-night package to Rhodes for a family of four, which now costs £1,928, departing on July 25 and staying in a four-star hotel.

The biggest discounts are on packages on charter flights, on which Olympic has committed to buying the seats, and to accommodation where the operator has already committed to buying the rooms. Some of the properties are exclusive to Olympic.

The company, along with several other operators, had already been discounting departures in June and September, but this is the first major operator to announce big cuts for the peak travel period.

There have been reports than Greek hoteliers have been forced to drop their rates by up to 50%, so holidaymakers prepared to travel independently might get even better deals by booking direct.

However, the consumer's association Which? last month advised its members considering travelling to Greece this year to book ATOL-protected package holidays. It said those booking direct with airlines and hotels should pay with a credit card or check that their travel insurance provided cover against supplier failure.