Speaking at a parliamentary hearing, Sarah Gilbert, professor of vaccinology at the university, said 8,000 volunteers had been enrolled for the Phase III of its trial into the vaccine, AZD1222, which was licensed to AstraZeneca.
"We're very happy that we're seeing the right sort of immune response that will give protection, and not the wrong sort," Gilbert said.
The project has started Phase III of the human trials to assess how the vaccine works in a large number of people over the age of 18, and how well the vaccine works to prevent people from becoming infected and unwell with COVID-19.
The race is on to develop a working COVID-19 vaccine, with fears that the pandemic could re-intensify towards the end of the year, in the northern hemisphere's winter season.
Kate Bingham, chair of the UK Government Vaccine Taskforce, said that, excluding the Oxford vaccine programme, she hoped there would be a breakthrough by early 2021.
Gilbert said she hoped that her Oxford vaccine would make progress earlier, but was not more specific as she said the timeline for when the vaccine might be ready depends on the results of the trial.
John Bell, Regius Professor of Medicine at Oxford University, said that Britain should prepare for not having a COVID-19 vaccine for the winter and encourage people to get their flu vaccinations to avoid "pandemonium" in hospitals.
"This whole epidemic has relied too heavily on assumptions that have turned out not to be true," he said.
"So my strong advice is to be prepared for the worst."