According to the study, published in Nature Medicine, the AstraZeneca vaccine is associated with a slight increased risk of Guillain-Barre syndrome (GBS) and Bell’s palsy in the 28 days after the first dose.
The Pfizer vaccine was linked to an increase in haemorrhagic stroke.
However, infection with Covid-19 was associated with a much higher risk of each of these conditions, as well as higher risks of other adverse events including encephalitis meningitis and myselitis.
Researchers urged members of the public to take up a vaccine if offered it.
Dr Martina Patone, Medical Statistician at the Nuffield Department of Primary Care Health Sciences at Oxford University and a co-lead author on the study, said it was “perfectly normal” for longer-term research to continue after a vaccine rollout had begun, using real-world data.
This research often looks at very rare events, occurring in fewer than one in 10,000 people.
The study found 38 additional cases of Guillain-Barre syndrome per 10 million people who had received a first dose of AstraZeneca vaccine, but 145 additional cases in those who had tested positive for Covid-19 in the previous 28 days.
These results were found after analysing health records of 32 million people in England, and replicated in Scotland.
Researchers also identified 60 extra hemorrhagic strokes per 10 million people who received a Pfizer vaccine, but this was not replicated in the Scottish data.
Authors said they could not be sure why this was the case, but it suggested the links between Covid-19 and AstraZeneca and GBS were the most “consistent”, and that the findings around hemorrhagic stroke could be less precise.
Covid-19 was also associated with a higher risk of other adverse neurological events, including 123 extra cases of encephalitis meningitis and myselitis per 10 million people, and 163 extra cases of myasthenic disorder.
The study authors urged people to take up a vaccine when offered it.
Julia Hippisley-Cox, Professor of Clinical Epidemiology and General Practice at Oxford University, and co-author, said: “We know the Covid-19 vaccines are very effective at reducing risks of severe outcomes from Covid-19 infection.
“Whilst there are some increased risks of very rare neurological complications associated with the Oxford-AstraZeneca vaccine, these are much smaller than the risks associated with Covid infection itself.
“However, these very rare conditions are very important to spot to ensure that clinicians know what to look for, aid earlier diagnosis, and inform clinical decision making and resource management.”
Aziz Sheikh, Professor of Primary Care Research & Development and Director of the Usher Institute at Edinburgh University, and another co-author, stressed the rarity of adverse events linked to the vaccines.
“I think the context is really important here,” he said.
“These are very rare adverse events, they're so rare that we’re having to report them per million population, that just reflects how rare this is.”
He added: “The risks are orders of magnitude higher if people get infected [with Covid-19].”