Testing will now expand to essential workers and their families in England
Mr Hancock greatly expanded the criteria for who can be tested for coronavirus as he sought to meet the "challenging" target of 100,000 tests a day by the end of the month.
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"Because capacity has now increased so substantially we are now able to expand who can get the tests.
He said "essential workers" in England and their families - based on criteria similar to those used for deciding who can still attend school - will be able to be tested.
Mr Hancock said: "From today, employers of essential workers will be able to go on gov.uk to get a test for any of their staff.
"From tomorrow, any essential workers who need a test will be able to book an appointment on gov.uk themselves, directly.
"This all applies for people in essential workers' households too who need a test.
"It's all part of getting Britain back on her feet."
Mr Hancock said the whole process would be free for those being tested.
Public to take part in additional testing to establish how many people have had the virus
Testing is also being used to establish how many people have and have had coronavirus.
Initially, 25,000 people would take part, with plans to expand it to 300,000 over the next 12 months.
Participants will provide regular samples taken from self-administered swabs and answer a few short questions.
Mr Hancock said letters had started to go out to the public and appealed to anyone asked to become involved to do so.
NHS contact-tracing app is undergoing testing
Mr Hancock said infrastructure was being put in place so that contact tracing could be rolled out on a large scale.
He announced that a new NHS contact-tracing app was undergoing testing.
Anyone who became unwell with coronavirus symptoms would be able to inform the NHS through the app, which would then inform other users they had had significant contact with.
Government on track to reach target of 100,000 tests a day
Professor John Newton said the Government is "on track" to reach 100,000 tests a day.
He said they have also introduced new types of tests and that three new lighthouse labs in Milton Keynes, in Manchester and in Glasgow will be able to process tens of thousands of tests per day.
He said: "We are currently on track to reach 100,000 tests a day.
“In fact, we're somewhat ahead of where we thought we'd be at this stage.
"We're going to have 48 of these pop-up facilities which can travel around the country to where they're needed most - for example, in care homes.”