The self-isolation period is expected to be cut from two weeks to 10 days – rather than the seven days it had earlier been hoped would be enough.
Ministers had wanted to halve the quarantine time to a week amid reports of low compliance and were expected to announce the plans last week.
Government sources denied any row between the two men yesterday, and said that a review into the quarantine period would report in ‘due course’.
Its conclusions are expected within the next two weeks but the source stressed that no decisions had yet been made.
However, it is understood that the original plan had been to cut the quarantine period to one week to boost compliance.
Dominic Cummings, Boris Johnson’s chief adviser, was reportedly pushing for quarantine to be slashed from 14 days to just seven
But Professor Chris Whitty, the Chief Medical Officer, is said to have blocked the move with a compromise struck to reduce self-isolation to 10 days
Ministers are now expected to opt for 10, rather than seven, days of isolation despite fears that this will not help more people abide by the rules.
The reduced period is to be made possible by increasing the use of rapid tests which will enable a person to stop self-isolating on the tenth day after a negative test on the eighth day.
But if they test positive on that date, they will be asked to continue self-isolating for a further eight days.
It comes amid growing concerns about compliance, with only 11 per cent of people abiding fully by the current two-week self-isolation rule, according to research by King’s College London in September.
However, there are understood to be concerns that the public will find it difficult to remember a more complex set of rules.
Reports yesterday suggested that Mr Cummings had been pushing for just a week of quarantine, but Professor Whitty had dug in his heels.
The planned change is a compromise after Professor Whitty refused to accept Mr Cummings’ proposals, the Guardian reported.
It said that a press release had been drafted to use the rapid tests to halve self-isolation to seven days.
But Professor Whitty is said to have been implacably opposed on public health grounds, arguing that the incubation period for the virus was too long to allow immediate testing and the rapid tests would fail to detect every infected person.
The proposal to test after eight days, with permission to leave the house on the 10th day, was ‘cooked up’ as a compromise, to placate Mr Cummings, the paper added.
The UK’s three devolved governments in Edinburgh, Cardiff and Stormont are being consulted on the new proposal and their agreement will be needed before the policy can be implemented, according to the paper.
They are understood to be seriously considering it to increase compliance but have concerns about the test’s accuracy.
Lateral flow tests can give results within half an hour but detailed data on accuracy has not been disclosed.
However, there are concerns that the test may not be able to pick up the virus before the carrier shows symptoms.
But the tests have been welcomed by ministers who have said that they could lead to an end to quarantine for travellers.
Transport Secretary Grant Shapps told the Airport Operators Association conference that the developments should encourage more people to fly.
He said: ‘I want you to know that we’ve been making very good progress on a test-to-release programme to launch once we’re out of lockdown.
‘This will consist of a single test for arrivals into the UK, provided by the private sector and at the cost of the passenger, allowing a much reduced period of self isolation.
A Government source said reports of a row were ‘nonsense’ and said that the review would report in due course.
A Number 10 spokesman said: ‘Self-isolation is a vital tool in our fight to suppress the virus, so work is ongoing on options to increase the number of people doing so, including reviewing the self-isolation time period.’