A mass coronavirus vaccination programme is still months away, says the lead scientist working on the Oxford University project.
Andrew Pollard, director of the Oxford Vaccine Group, said two human volunteers have been injected - one with a coronavirus vaccine candidate and one with a meningitis vaccine acting as a control.
The Oxford University programme is the first in the UK to develop a possible vaccine but more tests are needed to determine its effectiveness before it can be rolled out.
Prof Pollard said: "The reason we stuck with two volunteers is to make sure there are no unintended effects and we will monitor them very closely over the first few days.
"Then we will move on to some larger groups of individuals over the next few weeks."
Speaking on BBC Breakfast, he said the scientists didn't expect to see an immune response for the next 10 days or two weeks after the vaccine has been administered.
Prof Pollar said the volunteers injected with the vaccine will not be deliberately exposed to Covid-19, but will instead wait until they come across it in the community.
However, owing to the effectiveness of the lockdown, which has slowed the spread of the disease, it may be "some months" before they come into contact with the disease.
An effective vaccine would mean the human body is able to produce antibodies of Covid-19 which would fight off the disease.
This could help reduce the impact of the disease on the human population, and help allow for life to start returning to normal.
Prof Pollard said unlike other diseases, there is not yet a "human model" for Covid-19, meaning scientists do not know what is a safe dose to give volunteers in vaccine trials.
He added that testing the vaccine was not as simple as putting someone who has been vaccinated in the same room as someone suffering from coronavirus and is symptomatic.
"You are potentially putting those people at risk and we know people who have had large exposure to the virus, some have become extremely unwell - including some young people," he said.
"At this moment, we don't have a treatment for coronavirus so we would have to do this extremely carefully."
Experts are working to find an effective vaccine or drugs to treat the disease.
Prof Chris Whitty, the chief medical officer for England, said social distancing measures in the UK may have to remain in place until effective treatments for coronavirus are found, saying it was "very unlikely" that would be before the end of 2020.
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