On the Beach said the number of bookings it has received for summer trips to those destinations is more than double the level from 2019, before the coronavirus pandemic.
It partly attributed this to the fall in the value of the Turkish lira and Egyptian pound against sterling over that period.
The number of lira that can be bought for a UK pound has quadrupled from around eight in 2019 to 34 right now.
Holidaymakers visiting Egypt are receiving approximately twice as much local currency for sterling than they were before the virus crisis.
On The Beach said a sharp rise in flight capacity has also driven the rise in demand for holidays in Turkey.
There are an additional 1.2 million seats on flights from the UK to Turkey this year compared with in 2019, according to the tour operator. Annual flight capacity is expected to grow by another 1.6 million seats by 2025, reaching a total of five million.
Heathrow Airport announced on Friday that July was its busiest ever month for departures to Turkey, with more than 73,000 people flying to the country. Airline Jet2 recently revealed its flying programme to Turkey is three times larger than in 2018.
Turkey was the company’s third most-booked overall destination for summer holidays. The Canary Islands took top spot, followed by mainland Spain.
On the Beach chief customer officer Zoe Harris said: “The top location for holidaymakers this holiday season is the Canaries, followed closely by Spain.
“Spain had a slight decline in bookings last year, however this year it’s back with a notable increase in bookings compared to 2019.
“The destinations to watch out for are Turkey and Egypt. They are rising the ranks at a rapid rate of knots.
“We expect to see these two destinations to continue to rise and challenge for the Canaries top spot next year.”