An expert at Oxford University has also hailed the approval of an anti-body test a "major step forward."
A team of researchers in the city started testing a Covid-19 vaccine in human volunteers at the end of April.
More than 1000 people are expected to take part in the trial. Half are being given the vaccine candidate and the other half will receive a widely available meningitis vaccine.
Sir John Bell, regius professor of medicine, said "several hundred" people have been vaccinated and the challenge now is to be able to manufacture at scale once it is approved by the regulators.
He told Radio 4's Today programme: "We also want to make sure that the rest of the world will be ready to make this vaccine at scale so that it gets to populations in developing countries, for example, where the need is very great.
"We really need a partner to do that and that partner has a big job in the UK because our manufacturing capacity in the UK for vaccines isn't where it needs to be, and so we are going to work together with AstraZeneca to improve that considerably."
He rejected the idea of challenge therapy - that would deliberately infect healthy volunteers with coronavirus - and said there should be results on the vaccine trial by using normal exposure to the virus, if you keep your head down.
The team now want to start "phase 1/2 project," he added.
"And so far so good, and we're now starting to wait for an advocacy signal to see whether people who've been vaccinated, don't get the disease so that's the next step."
We're now starting to wait for an advocacy signal to see whether people who've been vaccinated, don't get the disease so that's the next step," Prof Bell said.
He also explained that the researchers had discussed deliberately exposing people to the virus, but the practicalities are complicated, as there is no treatment yet to to rescue people if they get sick.
He added that to check its effectiveness, you would need to give the virus to those most at risk, and the risk of them dying would be very high if it did not work.
Separately, Prof Bell said the development of a test to find out whether people have been infected with coronavirus in the past was "a good result".
The antibody test, developed by Swiss pharmaceutical giant Roche, has been approved by health officials and is likely to be rolled out to frontline workers first.
Sir John said antibodies "stick around probably for a year or two" adding that the Roche test was the "best approved test available on the market now."
But he said it was currently unclear whether having Covid-19 gave immunity against all future infection with the virus.
"What I think you can't for absolutely for sure say is that you would be protected in the future," he said, adding there were still improvements that could be made to antibody tests.
PIC by: Pool/PA Wire