A major study from Public Health England found last week that people who had caught coronavirus could be immune for at least five months.
That would mean that many people who have recovered from coronavirus could be immune until the summer when far more vaccine doses are likely to be available.
However, despite this, ministers told Parliament last week that vaccinations for people who have had Covid-19 should only be deferred for at least four weeks after the onset of symptoms.
Health minister Nadhim Zahawi told MPs: "The Joint Committee on Vaccination and Immunisation are the independent experts who advise the Government on which vaccines the United Kingdom should use and provide advice on prioritisation at a population level.
"Clinical decisions will be made for those who have suffered from a Covid-19 infection and it is likely that vaccination should be deferred until clinical recovery and at least four weeks after onset of symptoms."
That prompted senior Tory MP Sir Christopher Chope to say that anyone who has had the virus should not be prioritised in the vaccine rollout.
He said: "There was evidence published last week which shows that people for at least five months after they have been infected by Covid and recovered have antibody immunity.
"Therefore, applying the logic of people only having one jab – because to get everyone up to 70 per cent is better than getting some people up to 90 per cent – [it] may be the eight, nine or 10 million people who have had Covid in the past six months should wait for their jab to let others who have not had Covid go ahead."
PHE has been regularly testing tens of thousands of health care workers across the UK since June for new Covid-19 infections as well as the presence of antibodies, which suggest people have been infected before.
The health body's scientists found that naturally acquired immunity as a result of past infections provided 83 per cent protection against reinfection, compared to people who have not had the disease before. This appeared to last at least for five months from first becoming sick, PHE said.
Between June 18 and November 24, PHE scientists detected 44 potential reinfections out of 6,614 participants who had tested positive for antibodies. This represented an 83 per cent rate of protection from reinfection.
A Department of Health and Social Care spokesperson said that it planned to have vaccinated "tens of millions of people" by April but the "degree or length" of immunity of those recovering from Covid-19 was unknown.
The spokesperson said: “As with all new viruses, we don’t yet know the degree or length of immunity those who have recovered from coronavirus have.
"The most important thing is to vaccinate those who are most at risk from Covid, so we will continue to follow the science and advice from the JCVI and chief medical officers.
“The NHS is doing everything it can to vaccinate those most at risk as quickly as possible and more than 3.2 million people have already received the first dose.
"Tens of millions of people will be vaccinated by April and, as we accelerate our vaccination programme even further, it is absolutely paramount people across the country follow the rules and stay at home to protect the NHS and save lives.”