Government ministers are considering giving everyone in England a £500 payment if they test positive for Covid-19 in a desperate effort to improve rates of self-isolation.

The £450 million-a-week proposal, revealed in a 16-page paper obtained by the Guardian, comes after it emerged just one-in-four people who need to self-isolate for 10 days were actually doing it because of fears of being out of work.

The idea, which is not yet government policy, is reportedly the “preferred position” of Matt Hancock’s Department of Health of Social Care.

On Friday morning, environment secretary George Eustice said the £500 payment for people quarantining after testing positive for coronavirus was “under review”.

Speaking to Sky News, he said: “We have always kept it under review.

“We do need people, if they are asked to self-isolate because they have been contacted through our Test and Trace, we do need them to self-isolate.

“And, obviously, we always review the reasons why they might not.”

He added: “No decisions have been made on this. But, this is a dynamic, fast-moving situation with the pandemic.

“We are always keeping multiple policies under review.

“We have had a targeted £500 payment already for those who are on benefits to help them with the costs of staying at home when they are unable to work.”

Currently people forced to quarantine either because they have been infected with Covid-19, or have been in contact with someone who has it, can claim a £500 payment through the test and trace system.

But the report suggests the idea could be extended to millions of people who have missed out because they must be in work, are unable to work from home and are on certain benefits.

Aside from a universal £500 payment, alternative options include smaller lump sums or means-tested payments. Measures also proposed include a police crackdown on quarantine breaches and a nationwide programme of self-testing. The report comes as Covid-19 runs rampant in the UK with deaths topping 1,000 on a daily basis.

The report says: “Wanting to avoid self-isolation is now the single biggest reported barrier to requesting a test.”

A government source suggested it was just one of many options being discussed as part of improving stay-at-home compliance for those who had tested positive.

A Department for Health and Social Care spokesperson said they would not comment on leaks, but said: “We are in one of the toughest moments of this pandemic and it is incumbent on all of us to help protect the NHS by staying at home and following the rules.

“All local authorities costs for administering the test-and-trace support payment scheme are covered by the government, and each authority is empowered to make discretionary payments outside of the scheme.

″£50m was invested when the scheme launched, and we are providing a further £20m to help support people on low incomes who need to self-isolate.

“We also recognise the impact of the pandemic on people’s mental health and wellbeing which is why mental health services have remained open throughout the pandemic.”

The Resolution Foundation, a think tank which has previously calculated that only one in eight workers qualify for the financial support currently offered to those told to self-isolate, welcomed the proposal.

Researcher Maja Gustafsson said: “The current approach is not fit for purpose with statutory sick pay among the least generous of advanced economies and far too few people eligible for the £500 support payments.

“Swiftly putting in place a much more universal and generous system will make a real difference to controlling the spread of the virus.”