Instead, UK tourists are taking more trips to traditional favourites such as France, Italy and Spain, according to an analysis of nearly five million holidays by the Co-operative Travel company.
Bookings are 30% down to Egypt, 16% down to Tunisia and 11% down to Turkey, while Morocco, where bookings started the year strongly, has seen a 53% dip in recent weeks.
In contrast, France is up 31%, Italy up 15%, Spain has risen by 11% and Portugal is up 7%.
Co-operative Travel said cost as well as security concerns were a factor in choice of destination for Britons.
The company's managing director Mike Greenacre said: "The cost factor is best highlighted by the numbers of people switching between Turkey and Greece.
"Turkey hasn't experienced the problems faced by the other METT (Morocco, Egypt, Tunisia and Turkey) destinations, but seems to be suffering because people are comparing average prices to Greece, which is seen as offering a very similar type of holiday."
He went on: "In recent weeks we've seen prices tumble for certain destinations as operators look to fill excess capacity. For example, people booking now for a summer holiday in Turkey are paying an average of £567 per person, which is 12% less than earlier in the season. This is a huge saving; a reduction of £312 for a family of four."