Researchers believe they have made a breakthrough after discovering the jab could provide "double protection" against the virus, it has been reported.
The phase 1 trial in healthy adult volunteers showed the vaccine generated an immune response, with blood samples indicating it stimulated the body to produce both antibodies and "killer T-cells".
That's according to a source who told the Daily Telegraph that the combination of the two responses "will hopefully keep people safe", a source told the newspaper.
David Carpenter, chairman of the Berkshire Research Ethics Committee, which approved the Oxford trial and continues to work with scientists on amendments, said the team were "absolutely on track".
He added: "Nobody can put final dates ... things might go wrong but the reality is that by working with a big pharma company, that vaccine could be fairly widely available around September and that is the sort of target they are working on."
Health Secretary Matt Hancock said teams were working towards a "best case scenario" of a vaccine being made available some time this year, although conceded it was more likely in 2021.
Speaking on ITV's Peston on Wednesday evening, Mr Hancock said: "We're all working towards the best case scenario, we're all giving AstraZeneca and the team at Oxford, and the Imperial vaccine, every possible support, we're working with the other potential vaccines around the world, in America, and Germany, and the Netherlands.
"We're working with them to ensure that if they come off first, that we'll get access to them here.
"But this is an inexact science and it's at risk."
He said the most clinically vulnerable, such as the elderly, and healthcare workers would be the first to get the vaccine, and added that he is expanding the list of professionals who can legally vaccinate, which will include not just GPs but also technicians, nurses and pharmacists.
Nurses and pharmacists can already administer certain vaccinations without a prescription from a doctor.
The promising news on the vaccine comes as the Government is set to decide on whether to make changes to the local lockdown in Leicester, more than two weeks after stricter measures were imposed on June 30.
Ministers will look at the latest data on Thursday, with Mr Hancock promising that an announcement on the next steps will be made "as soon as is reasonably possible".
But the city's mayor Sir Peter Soulsby said on Wednesday that only 10 per cent of the city was showing higher transmission rates and branded the local lockdown as "unnecessary and unjustified".
In a report Sir Peter posted on social media on Wednesday, he said that new neighbourhood data showed the areas most affected by the virus were those with high levels of deprivation in the inner city.
He added: "Together with other local authority leaders throughout England, we have been asking for some weeks for neighbourhood data about the coronavirus testing in our areas.
"We have now received the first set of that data.
"This clearly shows that the areas most significantly affected by the virus are those with high levels of deprivation in the inner city.
"Given what this data shows, it is no longer possible to justify the continuation of the 'lockdown' across the remaining 90 per cent of the Greater Leicester area."
Mr Hancock told ITV's Peston: "The infection rate has come down in Leicester. It's still a lot higher than elsewhere. And, so, I don't want to prejudge a decision tomorrow (Thursday)."
Meanwhile, unemployment figures for July are due to be published on Thursday, while the latest NHS Test and Trace statistics will also be released.