People flouting coronavirus lockdown rules will be slapped with an initial £30 fine and could end up in court if they do not pay.
On Monday, Boris Johnson said tougher restrictions on people's movements during the crisis would be enforced by police and warned those ignoring them would be fined.
Officers will have powers to disperse gatherings under a ban on meetings of more than two people apart from those who live together.
On Tuesday, Mr Johnson's official spokesman said: "The Prime Minister issued a clear instruction on behalf of the Government on the actions the public are required to take to help prevent the spread of the virus, protect the NHS and save lives.
The punishment would be a fixed penalty notice initially set at £30 but "we will keep this under review and can increase it significantly if it is necessary to ensure public compliance".
"You would expect the police's focus to be dispersal of groups," the Prime Minister's spokesman said.
Failure to pay a penalty notice could be subject to criminal proceedings and a conviction, he added.
Regulations will be made by Thursday at the latest to allow police to issue fines under the 1984 Public Health (Control of Diseases) Act for England and Wales.
The emergency legislation going through the House of Commons will provide equivalent powers to Scotland and Northern Ireland.
Earlier, Sir Peter Fahy, former chief constable of Greater Manchester Police, told BBC Breakfast there was "a huge amount of clarification needed" on the rules.
Police chiefs warned of phone lines being inundated with calls after Mr Johnson's statement, with questions about what movements are still permitted.
West Midlands Chief Constable Dave Thompson said the force is "already receiving many calls on potential breaches of these arrangements" and said the public could ring 101 with information about large-scale breaches.
Prime Minister @BorisJohnson yesterday introduced significant social restrictions, which touch on everyone's lives across the West Midlands.@DaveThompsonCC has set out what you can expect from us during this time.
You can read his message here ⬇️ https://t.co/33jlUgGR7v
— West Midlands Police (@WMPolice) March 24, 2020
Asked how social distancing rules would be enforced by police, Martin Hewitt, chairman of the National Police Chiefs' Council (NPCC), told BBC Radio 4's Today programme: "Ultimately, if people do refuse to abide by the rules then we will need to enforce them."
However, he said the legislation has not been enacted yet.
The NPCC later said officers would not be deployed on patrol specifically to police social distancing rules but will "remain patrolling their communities as always".
Ken Marsh, chairman of the Metropolitan Police Federation, which represents officers in London, told Sky News the new measures will be a "real challenge" and "very difficult".
He added: "We will be dealing with it, but I'm not sure we will have the resources to be able to see it through."
John Apter, national chairman of the Police Federation of England and Wales, had previously told the PA news agency he "cannot imagine" how officers would police social distancing, adding: "I just cannot rationally think how that would work."