Millions of key workers and their households are now eligible for coronavirus tests as the government races to meet its 100,000 daily target by the end of next week.
These tests can be carried out from Friday.
NHS and social care staff, police officers, teachers, social workers, undertakers, journalists and those who work in supermarkets and food production are among those now eligible.
The announcement came as researchers at the University of Oxford began human trials for a potential coronavirus vaccine candidate.
Mr Hancock set out his plans for “easier, faster and simpler” testing so that more people can access a Covid-19 test to tell them whether they have the virus.
He said people can register for a test at www.gov.uk/coronavirus.
When some key workers tried to use the website on Friday morning, they reported being unable to access it.
A government source said this was due to "enormous" usage and had been brought in to manage demand.
A short while later, users reported being able to log in as normal.
People will then receive a text or email with an appointment at a drive-through centre or can request a home test kit, although the latter are currently in limited supply.
However, by 8.45am on Friday, the day's allocation of home test kits had already been met.
A help desk has been established to aid the process, while mobile units run by the Army are travelling around the country to where they are needed, such as care homes.
Test results from the drive-through sites will be sent out by text within 48 hours, and within 72 hours of collection of the home delivery tests.
At the daily Downing Street briefing, Mr Hancock said the capacity for carrying out tests was now “ahead of our plans”, with the ability to carry out more than 51,000 tests a day.
“Because capacity has now increased so substantially, we are now able to expand who can get the tests,” he said.
“Our ultimate goal is that everyone who could benefit from a test gets a test.”
Hancock says testing capacity vital to UK's coronavirus fightback
Essential workers will be able to book coronavirus tests direct, while companies will also be able to book them for employees.
The Health Secretary also said he was proud of the way the public had responded to the demands of the social distancing regime, and praised the police for their work in enforcing them.
Ahead of a weekend of warm and sunny weather, Mr Hancock said: “I’ve also seen reports of the police stopping people from having barbecues on the beach and making sure that people follow the social distancing rules.
“That’s because the rules are there for a reason and that’s because we need to follow the rules in order to protect the NHS and to slow the spread of this virus.”
Overnight, two RAF aircraft carrying 400,000 gowns but also masks and gloves arrived from Turkey at Brize Norton in Oxfordshire.
The NHS requires around 140,000 gowns each day.
A spokesperson for the Department of Health and Social Care said a further order of 140,000 gowns would be arriving in the UK from Myanmar in “the coming weeks”.
Also on Thursday, the number of people who have died in hospital with coronavirus rose by 616 to 18,738, but the total toll is likely to be several thousand higher when those who have died in care homes and the community are included.
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