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More than 200,000 people have signed the petition, which claims vaccine passports could be 'used to restrict the rights of people who have refused a Covid-19 vaccine,' meaning it could now be debated in Parliament.
Prime Minister Boris Johnson announced that the government would be reviewing vaccine passports - or vaccine certificates - earlier this week.
While it is not mandatory for people to take the vaccine when offered, it is strongly encouraged.
However, the petition states passports 'would be unacceptable' because they would have an effect on what people who refuse to have the vaccine can do.
Cabinet Office Michael Gove is currently in charge of looking at the scheme, which could also lead to the NHS Covid-19 app being updated to include proof of vaccination.
Matt Hancock also said the government planned to allow people to prove whether they've had the jab if it was demanded by other countries in order for them to travel there.
However, the review that has been announced is where they'll thrash out the details of what will happen on a domestic level.
Hancock told a Downing Street press conference: "I think it's best to allow that review to take evidence, to consider all of the broad range of issues, and then come to its conclusion.
"It's right we take our time to think about this."
However, the petition states: "We want the government to commit to not rolling out any e-vaccination status/immunity passport to the British public.
"The government must be completely clear to the public about the use of vaccine passports and their intensions, which will undoubtedly affect societal cohesion."
It's not just them, either.
Human rights group Liberty has also expressed concerns about the vaccine passports, and head of policy and campaigns Sam Grant told BBC News they could 'create a two-tier society where some people can access support and freedoms, while others are shut out - with the most marginalised among us hardest hit'.
He added: "The road out of lockdown can't ride roughshod over our rights.
"That's why we need the Coronavirus Act to be repealed, and replaced with strategies that provide support to help people to follow health guidance.
"That means rejecting proposals like immunity passports which are based on exclusion and division. Instead, we must work to bridge divides with strategies that protect everyone."
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