Most people agree that only those vaccinated should be able to fly when a coronavirus vaccine is freely available, according to a Sky News poll.
The findings also suggest there is work to do to convince the public, as nearly one-in-five say they are unlikely to get the jab.
And 11% say they could stop following social distancing after they get vaccinated, risking a possible increase in infections.
The results of the SkyNews/YouGov survey come as the first pictures of COVID vaccine appointment cards were released.
The card has space for the name of the vaccine, the dates administered and the batch number.
The government has insisted they are not meant to be seen as “immunity passports” that confer special privileges, and said there are no plans for such an idea.
But Sky’s poll of more than 1,700 people found 54% felt it would be acceptable to limit air travel to only people who have been vaccinated.
Some 29% said it would be unacceptable, and 17% were not sure.
For transport in general, such as buses and trains, around a third (36%) thought it would be okay to limit travel to vaccinated people.
The percentage in support of limiting access to restaurants was 39%, and 44% for cinemas.
Britain is the first country to approve the BioNTech/Pfizer vaccine and the first jabs will be given this week – in what some ministers have painted as a national triumph.
Despite it being signed off and showing 95% efficacy, a significant proportion of people are still hesitant – with 10% telling Sky News they are very unlikely to get it, and 8% fairly unlikely.
However, more than 70% of people are set to get the jab, with 49% very likely and 22% fairly likely.
About one in 10 are still unsure.
There may be concern that a small percentage appear to see the vaccine as a green light to ditch social distancing and other restrictions.
A total of 11% said they would probably not follow whatever rules are in place after taking the jab.
That may trouble health officials because even if people will not get sick after taking the vaccine, it is still unclear if the medicines stop people transmitting COVID-19.
There are likely to be millions waiting their turn in the UK’s vaccination queue for many months.
Nearly a quarter of people also said they would prefer to have the Oxford/AstraZeneca vaccine over the others once all are signed off.
That is despite it having a lower overall efficacy rate than the others – currently 70.4% – as scientists work out the optimum dosing method that could bump it up to about 90%.
Some 9% said they would prefer the BioNTech/Pfizer jab, 2% the Moderna, 38% had no preference and 27% did not know.
The Sky News/YouGov poll surveyed 1,706 adults online from 2-3 December. The figures have been weighted and are representative of all adults.