Police will impose heavy fines on anyone ignoring an instruction to stay home to curb the spread of Covid-19, the public is being warned, as a new law comes into force.

The home secretary, Priti Patel, vowed to get tough, after a detailed study found that just 18 per cent of people who have developed coronavirus symptoms have been following the rules.

The lack of compliance – amid surging infection rates – prompted the government to introduce the legal duty to self-isolate in England after a positive test, or if told to by the test-and-trace programme.

From Monday, fines for disobeying will start at £1,000, increasing “up to £10,000 for repeat offences and the most serious breaches”.

“These new measures are about saving lives. Everyone must take personal responsibility,” Ms Patel said.

“For those who fail to do so, the police will enforce the law. These new fines are a clear sign that we will not allow those who break the rules to reverse the hard-won progress made by the law-abiding majority.”

Boris Johnson also announced that low-earners who are unable to work from home and are losing income because of being told to isolate will receive £500 “support payments”.

But the cash will not be available until 12 October, ministers now say – while insisting they were “working quickly” with local authorities to get the scheme up and running.

Backdated payments have been promised, but the delay will fuel criticism that the law is tightening on people affected by the pandemic who do not have the necessary financial support.

The change comes as the prime minister faces a warning of “certain” defeat over imposing Covid-19 restrictions behind the backs of MPs, as opposition parties join up with Tory rebels.

Labour, the SNP and the Liberal Democrats are expected to back up to 60 Conservatives in a showdown vote on Wednesday that would give the Commons prior approval on coronavirus measures.

To enforce the new legal duty to self-isolate, test-and-trace call handlers will make more calls to people who have been told to remain home.

The police will also monitor compliance “in highest-incidence areas and in high-risk groups based on local intelligence”, the government said.

Reports of breaches made by members of the public would be acted upon and there would be prosecutions in “high-profile and egregious cases”.

Employers who force or allow staff to come to work when they should be self-isolating will also be targeted.

Anyone given a positive test result is required to self-isolate for 10 days after displaying symptoms or, if they do not have symptoms, after the date of the test. Household members must self-isolate for 14 days.

But people can also be instructed to stay home if the test-and-trace programme finds that they have had close contact with someone who has tested positive, regardless of whether they have symptoms.

Furthermore, if they develop symptoms and take a test, they must stay home even if that test delivers a negative result.