Biometrics could be used to confirm the identity of a person and match it with their jab record and in theory could allow travellers to move freely throughout the world knowing they cannot catch the virus.
The Government has said there are no plans for a UK vaccine passport.
But Andrew Bud, the chief executive of iProov, which is develops a biometric verification system, says the NHS would be "completely capable" of producing such a passport.
"Institutionally, if it's going to be part of your identity then there is only one organisation that you will trust to do that, and that's the NHS," Mr Bud says. "I don't think they'll trust anyone else with a vaccination status."
While UK start-ups such as iProov, Veridium and Onfido have all looked at how digital IDs for coronavirus immunity might work, the idea remains controversial.
"The goal may be to have an immunity passport system that is available to everyone, in practice this will likely be far from the case," according to Privacy International. "Health systems already exclude many people, or create unintentional hierarchies in society. Access to testing or a future vaccine will most likely follow the existing patterns of exclusion."
Beyond Britain, development of vaccine passes are well under way.
The World Economic Forum is developing a CommonPass system with the help of executives and officials from 52 countries, including three from Britain. The federation expects the app, which would develop a QR code that could be scanned by authorities, to roll out within the first half of next year.
Earlier in the month, United Airlines, Lufthansa, Virgin Atlantic, Swiss International Air Lines and JetBlue all said they would begin to offer the system to passengers. BA-owner IAG is working on a separate health pass, due to launch in early 2021, and tech giant IBM has developed a Digital Health Pass for companies and venues to verify customers' vaccine status.
Some countries are going further. In India, the government requires eligible recipients to register online with photo-identity documents, including Aadhaar, the country's digital ID. Israel is due to launch "green passports" through a mobile app on January 5 that will allow people who have either received the vaccines, recovered from Covid-19, or undergone a test to travel freely.
The World Health Organisation notes a proof of vaccine could be useful for monitoring the effectiveness of Covid vaccines.
"Having trustworthy and reliable proof of vaccination for COVID-19 vaccine will be essential for public health purposes, such as studies on vaccine effectiveness," a WHO spokesman said earlier this month.
But it seems unlikely the UK will push for such a pass. Michael Gove, the Cabinet Office minister, has said passports were "not the plan" and the focus instead was on mass vaccinations.
Although Britons may not require a government-backed immunity passport of their own to move around, private companies could make them use theirs. Mr Gove said individual businesses would "of course" have the "capacity to make decisions about who they will admit and why".
And although individuals may not be forced by the state to prove they've been vaccinated, they may need to in order to travel freely to certain countries. While they may never be mandatory, they could soon become an everyday reality.