The Government is promising £500 to some workers on low incomes who have to self-isolate.
In a significant toughening up of the regulations, ministers will impose a new legal duty on people to self-isolate if they test positive for the disease or are told to do so by NHS Test and Trace after coming into contact with someone with the virus.
Those on lower incomes who face a loss of earnings as a result of going into quarantine will be eligible for a one-off support payment of £500 to help them cope financially.
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With new cases of the infection doubling every week, Boris Johnson said the measures were necessary to control the spread of the virus and to protect the most vulnerable from becoming infected.
Just under four million people who are in receipt of benefits in England will be eligible for this payment, which will be available to those who are required to self-isolate from September 28.
Mr Hancock told Sky News' Sophy Ridge On Sunday programme: "We will support people who do the right thing and we will come down hard on people who do the wrong thing."
Local Authorities will be working quickly to set up these self-isolation support schemes. They are expected to be in place by October 12.
Those who start to self-isolate from September 28 will receive backdated payments once the scheme is set up in their Local Authority.
Boris Johnson has been desperate to avoid another nationwide lockdown amid concerns about the economic damage it will inflict just as activity was beginning to pick up again.
However, as of Tuesday, around 13.5 million people across the UK will be facing some form of local restrictions as the authorities grapple with the disease.