The Pfizer vaccine produces an "off the scale" immune response believed to protect against the Brazilian variant of Covid-19.
The biggest study on antibody and cellular immune factors suggests people are likely to be protected against the Wuhan, Kent and Brazilian types of coronavirus following two doses of the vaccine.
The research, led by the University of Birmingham and including Public Health England's Porton Down laboratory, found 98% of people aged 80 or over who had two doses of the Pfizer jab had a strong antibody immune response.
For the Birmingham study, 100 people aged 80 to 96 received their vaccine doses three weeks apart, before the UK adopted a policy of stretching the time between jabs to 12 weeks.
Published in The Lancet, the research found people who had previously had natural Covid-19 infection had a peak antibody response after just one Pfizer vaccination.
The antibody response in these people remained 28-fold higher even after the second vaccine dose.
Blood samples from all participants showed the original Wuhan strain was strongly neutralised after two doses of the jab.
While neutralisation reduced 14-fold when tested against the Brazilian variant, experts believe the very high immune response generated by the vaccine is enough to provide protection against that strain.
Professor Paul Moss, from the University of Birmingham and leader of the UK Coronavirus Immunology Consortium, told a briefing: "In terms of the variants and how we control them, people seem to be taking two broad approaches.
"One is we can develop another vaccine, a booster against these specific variants, so we perhaps have a South African booster vaccine - that's one approach and people are working on that.
"The other potential is that you boost your antibody levels so high from whatever vaccine you have that there's enough to go around and you cope with the variant.
"We've certainly seen in this paper that the antibody levels are so good, really after the first two weeks, that we are pretty confident that this should be very helpful against the Brazilian variant."
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Asked if he is surprised how well the vaccines have worked in older people, he said: "We were. When we sent these samples to Porton Down they said 'we can't give you results right now because we've got to dilute them because they're so high, they're off the scale'.
"The antibody levels were so high that they'd gone above the thresholds so they had to dilute them."
But he added it will be crucial to see how long antibody levels are maintained after people have had a Covid-19 vaccine.
He said: "It will be important to assess that and whether they wane at different rates in people of different ages.
"I think that's something that we have to watch out for."
Although the new study did not look at the Oxford University/AstraZeneca vaccine, Prof Moss said the evidence for the jab is that "it's very, very effective".
He added: "The UK has a strong portfolio of vaccines - Pfizer, AstraZeneca, we've got Moderna coming very soon, and Novavax as well.
"So yes, I think it's possible that we can have very broad vaccine coverage across the UK very quickly."
