Phase III will assess how the vaccine works in large numbers of people above the age of 18, and how well the vaccine prevents people becoming infected and ill with COVID-19.
It said that testing would also include a paediatric trial and that it was engaging with worldwide bodies, including the World Health Organization, for the fair allocation and distribution of the potential vaccine around the world.
"We are scaling up on a conservative basis of about 4 to 5 million doses a month to begin with", Chief Executive Adar Poonawalla told Reuters, adding the company was in discussions with AstraZeneca. "And that's what we're hoping for".
Phase one, which began in April, involved just over 1,000 adult volunteers aged 18-55, being inoculated, following promising results on six monkeys in the USA in late March.
Phase II will recruit up to 10,260 people, and expand the age range of participants to include the elderly and children, those aged over 56 and those between 5 and 12 years old.
Andrew Pollard, the head of the Oxford Vaccine Group, said: "The clinical studies are progressing very well and we are now initiating studies to evaluate how well the vaccine induces immune responses in older adults, and to test whether it can provide protection in the wider population".
More than 10,000 people will eventually be enrolled in the study.
A top USA scientist said on Wednesday that governments should not count on a successful vaccine against COVID-19 being developed anytime soon when deciding whether to ease restrictions imposed to curb the pandemic.
The objective is to assess the immune response in people of different ages, and see if there are any differences in how the young and old react to the vaccine.
ChAdOx1 nCoV-19 is made from a weakened version of a common cold virus from chimpanzees that has been genetically changed to make it impossible for it to grow in humans.
This has been combined with genes that make proteins from the Covid-19 virus (SARS-CoV-2) which play a key role in the infection pathway of the SARS-CoV-2 virus.
A small study in monkeys offers a note of caution: Teams from Oxford and the U.S. National Institutes of Health found the vaccine protected against pneumonia but didn't eliminate the coronavirus in the nose.
Pharmaceutical company AstraZeneca said it had orders for at least 400 million doses and would begin delivering them in September if the trial was successful.
The United States has secured nearly a third of the first 1 billion doses planned for AstraZeneca's experimental Covid-19 vaccine by pledging up to US$1.2 billion (RM5.22 billion), as world powers scramble for medicines to get their economies back to work.
In Scotland, the University of Glasgow will support the trials in collaborations with NHS Greater Glasgow and Clyde.
Dr Jennifer Armstrong, medical director of NHS Greater Glasgow and Clyde, said: "We're proud to have NHS Greater Glasgow and Clyde join the global effort in finding an effective vaccine for Covid-19".