Ministers in the UK are drawing up plans to give people greater financial support if they are forced to self-isolate after testing positive for Covid-19, amid fears that some are ignoring the rules because they cannot afford to miss work.

But allies of Rishi Sunak, chancellor, rejected as “bonkers” one idea that people should be paid a one-off flat rate of £500 to self-isolate, a scheme that would be vastly more expensive than the current one.

According to leaked documents obtained by the Guardian, the scheme would cost £453m a week, 12 times the more limited compensation currently offered in England.

“It’s the first we’ve heard of it and frankly it’s bonkers,” said one aide to the chancellor. However, ministers recognise there is a problem that needs to be resolved to keep the pandemic under control.

George Eustice, environment secretary, told the BBC’s Today Programme on Friday that he had not seen the document and was not aware of any changes being planned to the current system. But he added: “Whether that should be reviewed and changed and expanded is something that is always kept under review.”

The proposed change is thought necessary because a government survey found that only 17 per cent of people with symptoms were coming forward to get a test, owing to fears that a positive result could stop people from working.

Mr Eustice said that under the previous tiered system of regional lockdowns there were concerns about compliance, with some members of the public “reluctant” to isolate when they came into contact with someone who tested positive.

“At the moment we are in a full lockdown so everybody should be staying at home and generally they are and we are starting to see the prevalence of the virus start to go down as you would expect,” he said.

“There is a question as we start to emerge from the lockdown and go into a new phase, how do we ensure during that exit from the lockdown that people who are asked to isolate do so.”

According to the leaked document, the universal payment is the “preferred position” of the Department of Health. Another option was a payment to anyone on less than £26,495.

Currently those eligible for discretionary payments or the test and trace support payment receive a £500 lump sum in addition to benefits and sick pay. But only those on a low income who cannot work from home and receive one of seven means-tested benefits are eligible for the payment, which is administered by local councils.

There have also been high rejection rates for those who apply for the payment, according to figures obtained by Labour and shared with the BBC. Between October and December last year, three-quarters of the 49,877 applications were rejected, the data showed.

The health department said local authority costs for administering test and trace support payments were covered by central government, and each council was empowered to make discretionary payments outside the scheme.