It comes a week after the government announced that a new COVID-19 antibody test to tell whether someone has had the virus has been approved for use in the United Kingdom after being found to be 100 percent accurate.
The new test, which has been proven effective in clinical settings, does not need to be sent to a laboratory to be processed and can return results within 20 minutes.
The tests were heralded by Prime Minister Boris Johnson as being a "game-changer" for lifting lockdown because someone who finds out they have antibodies can be "safe and confident in the knowledge that you are most unlikely to get it again". Three domestic-made tests are also being assessed.
They will initially be offered to NHS staff and care workers but some patients will be able to request them via their doctors.
Given London's population, that would mean 1.5 million people in the capital have had the virus.
At the daily press briefing, Hancock said certificates were being looked at for people who test positive for coronavirus antibodies.
Separately, the health department announced that the trial of the new, rapid test to see whether people were carrying the virus had begun in Hampshire. Germany, one of the first countries to order millions of tests from Swiss drug giant Roche, said it would not use them until they had been debated by the country's top ethicists.
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The swab test will be carried out in a number of A&E departments, GP testing hubs and care homes in the county in a trial lasting up to six weeks.
A test to determine whether people have been infected with coronavirus in the past has been approved by health officials and will be rolled out across the country from next week.
In contrast to the widely used PCR tests, which need be processed at different temperatures, the loop-mediated isothermal amplification (LAMP) swab test does not require a change in temperature to detect results.
England's deputy chief medical officer, Professor Jonathan Van-Tam, last week promised the tests would be rolled out "rapidly". Currently, he said, 90% of results come within 48 hours, and nearly half within 24 hours.
On the Government's "test, track and trace" programme, Mr Hancock sought to play down the importance of the delayed app in the contact tracing process.
For care staff, the roll out will be phased across regions, with the Government and local leaders to decide the most appropriate places to start.
Mr Hancock said: 'The technology is an important part, but it is not the only part'. "They are distinct but complementary, it's perfectly OK - in fact possibly advantageous - to introduce the one before the other", he said.