Certification could involve people being either vaccinated, having had a recent negative test or having previously been infected, the PM said.
Baroness Chakrabarti told BBC Radio 4's Today programme: "It's one thing to have a passport to travel internationally, that is a privilege, even a luxury, but participation in local community life is a fundamental right."
She added: "To introduce two queues at the cinema, two queues at the football stadium going forward, is to introduce checkpoint Britain that so many of us just do not want."
The Labour peer, a former head of human rights organisation Liberty, said passports could see "policing power" given "to every bouncer or unscrupulous boss".
"It's a recipe for bullying, it's a recipe for corruption, it's a recipe for discrimination and it's not what we sacrificed so much for as a community over the past year," she said.
The plan could also "scupper things" for hospitality venues who are trying to reopen, Emma McClarkin, chief executive of the British Beer and Pub Association, said.
She told BBC Breakfast: "It is a difficult process for us to implement... and yet today we have not had a consultation with the government about how we would do this in pubs."
A cross-party group of MPs and peers have signed a pledge saying they "oppose the divisive and discriminatory use of Covid status certification to deny individuals access to general services, businesses or jobs".
The issue has brought together some unlikely allies, with many of Mr Corbyn's former shadow cabinet joining the lockdown-sceptic Covid Research Group of Conservative MPs in backing the campaign.
Accusing the government of "creeping authoritarianism", Liberal Democrats leader Sir Ed Davey said: "As we start to get this virus properly under control we should start getting our freedoms back. Vaccine passports - essentially Covid ID cards - take us in the other direction."
Sir Graham Brady, who chairs the 1922 Committee of backbench Tory MPs, added: "With high levels of vaccination protecting the vulnerable and making transmission less likely, we should aim to return to normal life, not to put permanent restrictions in place."
Privacy campaigning organisation Big Brother Watch also signed the pledge and published a report arguing against the measure.
The group's director, Silkie Carlo, said: "We are in real danger of becoming a checkpoint society where anyone from bouncers to bosses could demand to see our papers. We cannot let this government create a two-tier nation of division, discrimination and injustice."
In the campaign group's report - entitled "Access Denied" - it said if certificates were brought in, it would be "the first policy for decades that could see segregation imposed throughout the population".
Unlikely coalition hardens opposition
Political opposition to the idea of Covid passports is hardening among some, even before the government announces its plans.
The unlikely coalition of more than 70 MPs and peers of varying political colours shows that the issue crosses party lines.
Boris Johnson has talked increasingly openly about the idea in general, perhaps trying to prepare people for what is to come.
But will principled objections to asking people to prove their Covid status scupper the prime minister's plans?
That depends on exactly what is proposed and how Labour and rebellious Conservatives respond.
If and when it comes to a vote in the House of Commons, the government can't be sure at this point that it will have the support it needs.
The campaign comes after Labour leader Sir Keir Starmer this week said the use of Covid passports to decide whether people can enter pubs would go against the "British instinct".
A government spokeswoman said: "The review is considering a range of issues, including the ethical, equalities, privacy, legal and operational aspects and what limits, if any, should be placed on organisations using certification."
Meanwhile, the prime minister is preparing to give an update on the UK's Covid situation on Monday.
He is expected to confirm that data suggests the next stage of lockdown could ease in England on 12 April and that a traffic light system could be implemented for foreign travel, with countries being categorised as red, amber or green.
More than 31 million people have received the first dose of a coronavirus vaccine and more than 4.5 million have had a second dose, according to Thursday's daily figures.
The figures also show there were a further 51 deaths within 28 days of a positive coronavirus test, bringing the total to 126,764. Some 4,479 new cases have been recorded.