The poll indicated that acceptance is highest among people aged over 65 (89%), who have been offered Covid-19 jabs ahead of most younger people.
The figure falls to 67% for 18-24-year-olds, but London City Airport which commissioned the research, believes it will rise as vaccines are rolled out further.
Prime Minister Boris Johnson has pledged that all UK adults will be offered their first dose by the end of July.
Under his road map, international holidays could be permitted for people in England from May 17.
Currently, anyone who gets a jab is given a vaccination card and has their medical records updated.
But the Government is considering the introduction of vaccine passports as a specific way for people to prove their status, potentially through the existing NHS app.
There are concerns about ethical and legal issues, but Health Secretary Matt Hancock has told MPs "it is clear" that individuals will need a way of showing that they have had a jab.
The European Union has confirmed plans for a "digital green pass" to allow people to travel into the bloc by showing they have been vaccinated or had a negative Covid test.
The London City survey of 2,014 adults also indicated that 72% of frequent flyers want to return to travel as soon as restrictions are lifted.
Some 71% of those polled believe travel should be allowed between countries that have the virus "under control".
Civil Aviation Authority data shows just 6,474 passengers travelled through London City in January, down 98% on the same month last year.
The airport's chief executive Robert Sinclair said: "After the weakest first quarter that anyone in the industry can remember, the survey results show that the Prime Minister's road map has given British people hope again and it is very pleasing to see that so many see travel as a priority as restrictions are eased.
"It has also given our airline partners confidence to schedule services throughout the summer and I am delighted that we will be able to connect travellers to so many destinations across the UK and Europe for the most well-deserved summer holiday they will ever have.