The Labour leader indicated that there could be opposition to the idea amongst the public if death rates are near zero and hospital admissions are very low.
It comes as hospitality and retail bosses warn that the use of vaccine passports or certification for customers entering venues could face “legal concerns” and create enforcement problems for businesses.
Sir Keir said: “My instinct is that, as the vaccine is rolled out, as the number of hospital admissions and deaths go down, there will be a British sense that we don’t actually want to go down this road.”
Speaking to the Telegraph, he added: “I think this is really difficult and I’m not going to pretend there’s a clear black and white, yes-no easy answer on this.
“It is extremely difficult.
“My instinct is that… (if) we get the virus properly under control, the death rates are near zero, hospital admissions very, very low, that the British instinct in those circumstances will be against vaccine passports.”
Last week, Prime Minister Boris Johnson said that pubs and other venues could use vaccine passports, before backtracking slightly to clarify that this may only be introduced once all UK adults have been offered a vaccination.
However, Sir Keir voiced his opposition to the idea that landlords could be allowed to decide for themselves, telling the Telegraph: “I think this idea that we sort of outsource this to individual landlords is just wrong in principle.”
Asked if he feels uncomfortable with the new Covid laws introduced, he explained that current restrictions should not be in place for longer than they are necessary.
“If that was a long-term proposition I’d be very, very worried about it and I would be fighting it tooth and nail,” he said.
“Nobody wants these restrictions, nobody enjoys living under these restrictions, and they shouldn’t be in place for a moment longer than is absolutely necessary.”