The trial is currently running at two hospitals with seven patients.
Researchers in Oxford are testing the effects of potential drug treatments for patients admitted to hospital with the virus.
There are currently no specific treatments for the coronavirus and it's possible some existing drugs used for other conditions may have some benefits.
Scientists say the randomised evaluation of Covid-19 therapy (recovery) trial will provide doctors and the health service with information they need to determine which treatments should be used.
The treatments initially included in the study have been recommended by an expert panel that advises the chief medical officer in England.
They are Lopinavir-Ritonavir, which is normally used to treat HIV, and the steroid dexamethasone, which is used in a wide range of conditions to reduce inflammation.
The side effects and safety of both drugs are already well known.
Other potential treatments will also be assessed by the trial in the future.
Peter Horby, professor of emerging infectious diseases and global health in the Nuffield department of medicine, and chief investigator for the trial, said: "There is an urgent need for reliable evidence on the best care for patients with Covid-19.
"Providing possible new treatments through a well-designed clinical trial is the best way to get that evidence."
He added: "All patients will receive the standard full medical care, regardless of which treatment group they are placed in."
Adult inpatients who have tested positive for Covid-19 in NHS hospitals, and not been excluded for medical reasons, will be offered the chance to take part in the trial.
Participants will be allocated at random by computer to receive one of the two drugs being studied or no additional medication.
This will enable researchers to see whether any of the possible new treatments are more or less effective than those currently used for patients with the virus.
Martin Landray, professor of medicine and epidemiology at the Nuffield department of population health, and deputy chief investigator, added: "The streamlined design of this clinical trial allows consenting patients to be enrolled in large numbers easily and without compromising patient safety or adding significantly to the workload of busy hospitals and their staff.
"In this way we can rapidly assess the value of potential treatments for Covid-19 and provide reliable information on the best ways to treat patients with this disease."
Chief medical officer Professor Chris Whitty and NHS England medical director Professor Stephen Powis have written to NHS trusts in England asking them to fully support the new trial.
The trial opened on March 19, and is currently running at two hospitals with seven patients.
Researchers are aiming to roll it out to more than 150 hospitals over the next two weeks, hoping to eventually enrol thousands of participants.