Travel firm Thomas Cook says 48% of their holiday bookings for peak season are to destinations outside the bloc, up 10% on the same time last year.
Turkey has leapfrogged Greece to become the second most popular venue after Spain.
Tunisia is another non-EU destination faring well, with package trip bookings doubling year-on-year.
Thomas Cook says the uncertainty over Brexit has led tourists to delay choosing where to go but many seem to want to avoid the usual European countries.
A survey found that holidaymakers regarded taking an overseas summer holiday as “very important”, with the majority saying they are more likely to holiday abroad this year than in 2018.
Will Waggott, chief of tour operating for Thomas Cook, said: “Britain may be living through unique times from a political perspective, however our desire to holiday abroad is clear.
“Thomas Cook’s 2019 Holiday Report reveals that the political turmoil is having an impact in other ways, revealing itself in a clear shift to non-EU countries and a growth in all-inclusive.
“Turkey has already overtaken Greece to claim the No 2 spot of most desirable summer destinations and Tunisia is working its way back up the popularity stakes as it re-establishes itself as a hotspot for British tourists.” The survey also revealed the decline in holiday romances for the younger generation.
Seven in 10 of 18 to 35-year-olds have never had a holiday romance and 50% say they have no interest in having one.
Earlier this year The Office for National Statistics revealed a huge year-on-year rise to 19,000 visits to Turkey in the first quarter of last year. They also revealed a 2% fall in visits to Europe.
Another trend showed more parents were staying home and letting grandparents take kids away.