Public Health England will start evaluating the drug next week.
Its researchers have helped create an exact replica of Covid-19 for use in the testing process.
Now, trials of a coronavirus vaccine - developed by Oxford University - could begin within the next month, according to the Government's health agency.
Permission was granted after similar vaccines developed for other diseases were proved safe in human trials.
Human testing could happen well ahead of the usual time frame for drug development, but first - it will be tested on animals next week.
Professor Adrian Hill from Oxford's Jenner Institute - which only began working on the drug in January - says there will be an accelerated pathway to get it deployed to save lives.
Professor Hill told the Guardian: "We are conscious that a vaccine is needed as soon as possible and certainly by June-July when we expect a big peak in mortality.
He added: "This is not a normal situation. We will follow all standard trial safety requirements but as soon as we have a vaccine that's working we anticipate there will be an accelerated pathway to get it deployed to save lives.
"The more vaccine we can provide the sooner the better."
Earlier this month, Anthony Fauci, the director of the US's National Institute of Allergy and Infectious Diseases, said he expected it would be at least 12 to 18 months before a coronavirus vaccine is widely available.
The Jenner Institute said it had based the drug on an "adenovirus vaccine vector" based on an adenovirus isolated from a chimpanzee.
An adenovirus is a group of viruses that typically infect membranes of the eyes, respiratory tract, urinary tract, intestines and nervous system.
The Jenner Institute said: "Chimpanzee adenoviral vectors are a very well-studied vaccine type, having been used safely in thousands of subjects, from one week to 90 years of age, in vaccines targeting over 10 different diseases."
It said among its advantages is that it can "generate a strong immune response from one dose" and is safe to use on people with pre-existing conditions such as diabetes.
Boris Johnson revealed at a press conference on Thursday that the first British patient had been put in a randomised trial for a treatment for coronavirus.
The Prime Minister also described the Government's plans to purchase antibody tests on a massive scale to detect if someone has had the disease as "a game changer".
Mr Johnson said "hundreds of thousands" of kits could be bought if the tests prove effective, with negotiations currently ongoing.
The human body produces antibodies when it fights an infection, so by measuring antibodies in the blood doctors can detect whether someone has had the infection previously.
PHE said understanding who has previously had Covid-19 will allow it to refine its estimates of how many people in the population will be affected and the rate of spread.
First patient recruited to RECOVERY today @OUHospitals - randomised open-label multicentre clinical trial to investigate drug treatments for #COVID-19. Contact your local clinical research network to be a trial centre. @RN_salbee @RichardHaynes3 @PeterHorby @MartinLandray— Katie Jeffery (@KatieJeffery10) March 19, 2020