Boris Johnson has warned that people could be hit with a £10,000 fine if they refuse to self isolate.
In a tough move, ministers will impose a new legal duty on people in England to self isolate if they test positive for the disease or are told to do so by NHS Test and Trace.
And the new law may be rolled out in Scotland too.
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.
With new cases of the infection doubling every week, Johnson said the measures were necessary to control the spread of the virus and to protect the most vulnerable from becoming infected.
The new regulations will come into force in England on September 28. UK Government ministers are talking with the devolved administrations in Scotland, Wales and Northern Ireland about extending the rules.
Johnson said: “The best way we can fight this virus is by everyone following the rules and self-isolating if they’re at risk of passing on coronavirus.
“And so nobody underestimates just how important this is, new regulations will mean you are legally obliged to do so if you have the virus or have been asked to do so by NHS Test and Trace.
“People who choose to ignore the rules will face significant fines. We need to do all we can to control the spread of this virus, to prevent the most vulnerable people from becoming infected, and to protect the NHS and save lives.”
Fines will initially start at £1000 rising to £10,000 for repeat offenders and for “the most egregious breaches” including those who stop other people from self-isolating, such as an employer who requires a staff member to come into work in violation of an order.
The penalties are in line with those for people who fail to quarantine for 14 days after returning to the UK from a country not on the list of low risk nations.
Officials said NHS Test and Trace would be in regular contact with individuals told to self-isolate and would report any suspicions that people were not complying to the police and local authorities.
Police will also check compliance in Covid-19 hotspots and among groups considered to be “high-risk” as well as following up reports from members of the public of people who have tested positive but are not self-isolating.
Prosecutions could follow in “high-profile and egregious” cases of non-compliance. There will be specific exemptions for those who need to escape from illness or harm during their isolation, and for those who require care.
By Tuesday, when the measures come into force, around 13.5 million people in the UK will be living under some form of additional coronavirus controls.