One in five holidaymakers believe being outside of the EU will make it harder to combat terrorism both abroad and at home in the UK.
And just under one in 10 say they are worried they’ll be treated negatively while on holiday following the Brexit vote.
But a survey of 1,091 Brits by Travelzoo, on 28 and 29 June, found 81% said the EU referendum has had no impact on their willingness to travel this summer.
Only 3% plan to cancel their holidays due to concerns about the current value of the pound.
Almost half of UK travellers (47%) have concerns regarding additional holiday costs in the coming months and years, and around a third of respondents fear the cost of travel insurance (31%) and mobile roaming charges (34%) will rise.
Travelzoo is reporting increasing demand for all-inclusive holidays, with 26% of the respondents saying they would be more likely to go all-inclusive this year.
Joel Brandon-Bravo, UK Managing Director of Travelzoo, said: "The stoic British spirit has prevailed and it’s incredibly positive to see people still pushing ahead with their holiday plans. However, for this to continue we urge the UK government to act quickly to resolve uncertainties around visa restrictions and other possible changes impacting travel.
"If they react slowly, and tourism is pushed down the list of priorities, British holidaymakers could be facing more expensive overseas holidays, and consequently we could see a dip in travel.
"First and foremost, we need reassurance from those negotiating our exit from the EU that tourism will be a high priority. We have to understand how an independent UK can operate in the European Common Aviation Area, otherwise we’ll be living in a world of reduced competition, reduced routes and higher travel prices. Action is needed now.
"From talking to several travel companies, I would also advise booking soon. The fall in the pound will take time to filter through into higher costs for flights and cruises but a sustained lower pound will eventually cause a price hike."
