President Donald Trump is considering introducing regulations to force foreigners to reveal their passwords for social media accounts, phone contacts and political ideologies before being allowed into the country, according to US reports.
A survey of 1,012 UK adults by travel search engine Kayak.co.uk found more than half (51%) would not agree to the measures, while 29% said they would do so if required but would "not feel comfortable".
Almost two-thirds (63%) described the rules as an "invasion of their privacy".
The research indicates that introducing extreme vetting could create further problems for the US tourism industry.
The number of UK travellers visiting North America decreased in the month Mr Trump became president, in contrast to other parts of the world.
Some 230,000 people visited the continent from the UK in January, down 17% on the same month last year, according to the Office for National Statistics (ONS).
Mr Trump has attempted to introduce a travel ban aimed at people from several Muslim-majority countries, which has run into trouble in the US courts.
Kayak travel expert Suzanne Perry said: "The new presidency and the border control rules he has already introduced have had a very negative impact on demand for travel to the US. Formerly one of Brits' favourite destinations, interest is hugely down in just one year.
"As the research shows, introducing further rules such as requiring visitors to hand over social media passwords would have a strong, additional impact on Brits' likelihood to visit the country and have further negative consequences for the US tourism industry as a whole."