Boris Johnson has said people could be fined if they flout new lockdown rules that will be brought in when a nationwide “track and trace” system is launched.
People will soon be notified if they have been in contact with anybody who has tested positive for coronavirus.
“Track and trace” will utilise a new app and a conventional tracing system that uses phone and email to alert people who may have been infected.
The system will rely on Brits staying at home for 14 days if they have had a possible contact with someone who is ill from COVID-19.
Tory MP Greg Clark asked the prime minister during a Liaison Committee meeting on Wednesday if it will be law or advice that will compel people to stay at home during the “track and trace” phase of lockdown easing.
Johnson said: “We will be asking people stay at home and if they don't follow that advice, we will consider what sanctions may be necessary.”
Clark asked if the penalty would be issued by the police or by civil authorities, to which Johnson replied: “Whatever is appropriate.”
The PM added: “To begin with we are asking people to do it as a matter of course if contacted by an NHS tracker or tracer.
“And if you're told you have been less than 2 metres away from someone has tested positive for coronavirus you should self-isolate.”
He added: “If people don’t we will consider bringing in financial sanctions.”
The prime minister admitted self-isolating would be a “grave imposition” for some but it was needed so the country could move forward and ease restrictions.
He added people who developed symptoms would be given tests and if they had the infection they could leave home after seven days instead of 14.
Johnson said: “We are relying very much on the common sense of the public to recognise the extreme seriousness of this.
“This is our way out, this is our way of defeating the virus.”
The PM said the government would be constantly reviewing cooperation compliance from the public to decide if fines were necessary.
Earlier in the meeting, Johnson was warned by Labour’s Yvette Cooper his handling of the Dominic Cummings crisis may mean people flouted the rules and public health messaging would be harder.
The PM has come under pressure to fire his chief adviser after he travelled 260 miles from London to Durham during the lockdown.
Cooper told Johnson he had “a choice between protecting Dominic Cummings and the national interest” by either choosing to fire him or keep him on.
Tory MP Simon Hoare also asked if keeping Cummings would undermine the public health message which would mean people ignored lockdown measures.
The PM responded he "did not think that was true".