Health Secretary Matt Hancock, speaking at the government's daily coronavirus update, said the result is "based on a sample" and that antibody tests are needed at a "larger scale" before the public can know whether they've had Covid-19.
As such, he said the government had reached a deal on the supply of 10 million commercial antibody tests which will be rolled out in a "phased way" from next week.
The tests, which reveal whether a person has had Covid-19 by checking if they have coronavirus antibodies, will be "free for people who need them" and priority will be given to NHS staff and care workers.
Mr Hancock warned, however, "we’re not yet in a position to say that those who test positive in these antibody tests are immune from coronavirus".
But he said "insights these antibody tests provide will be crucial" as understanding of the virus grows - "they can help us to understand how our bodies react to coronavirus and how its spread across the country".
The deal which was reached following negotiations between the government and pharmaceutical firms Roche and Abbot.
Mr Hancock said devolved administrations of Wales, Scotland and Northern Ireland will decide how to use their test allocation.
Ministers are also awaiting results of a trail being carried out from today which, if successful, will mean tests can show whether a person currently has coronavirus, within 20 minutes.
Up to 4,000 people of all ages and backgrounds will participate in the pilot, which will run for up to six weeks.
ITV News Correspondent Paul Davies gives an update on the lockdown
It will be led by Hampshire Hospitals NHS Trust, and trained health professionals will take a swab and process the results on-site.
Mr Hancock said: "It doesn’t need to be sent to a lab to be processed and so you get the result on the spot typically within around 20 minutes.
"It’s already proven effective in early trials and we want to find out if it will be effective on a larger scale.
"We’ll monitor its effectiveness very closely and if it works we’ll roll it out as soon as we can."
The health secretary says an effective "testing regime will be our guiding star" as the UK moves further out of lockdown.
"Its the information that helps us to search out and defeat this virus," he added.
The UK is working to further ramp up its testing capabilities so that a system of "test and trace" can be implemented to track where coronavirus is in the country.
He said 25,000 contact tracers - made up of call handlers and medical professionals, will be hired by the start of June to trace contacts by emailing and phoning contacts of coronavirus patients.
He said the staff will be able to trace up to 10,000 contacts a day.
He told the Downing Street press conference: “The technology is an important part, but it is not the only part.”
He said trials of the app in the Isle of Wight had shown the human contact tracing elements were also important so people can understand the consequences of what is required if they have been near someone with coronavirus.
“The app is, as you know, working in the Isle of Wight, we want to make sure that this whole system lands well and supports the ability, safely, to make changes to social distancing rules,” Mr Hancock said.
It was earlier revealed at least 36,042 people have died with coronavirus, an increase of 338 from yesterday, according to the latest figures from the Department of Health.
Minutes before the press conference began, a Downing Street spokesman announced overseas health and care staff will be exempt from the fee levied on migrants to pay for use of the NHS.