Matt Hancock has said England is “clearly on track” to further ease the coronavirus lockdown, with the hope pubs, restaurants and hairdressers could reopen as early as July 4.

On Sunday, the Health Secretary promised the next steps would be set out this week, along with any alteration to the two-metre social distancing guidance.

With the two-metre rule placing severe constraints on the hospitality sector, it looks increasingly likely to be reduced as long as other mitigations – such as face coverings – can be used to help prevent a second wave of Covid-19 infections.

Ministers believe that cases of coronavirus are sufficiently low after three months of lockdown that a greater reopening can take place in order to revive the ailing economy.

Mr Hancock told Sky’s Sophy Ridge On Sunday: “We’re clearly on track for that plan because (of) the number of cases coming down, and the plan does refer to hospitality and some of the other things that are closed that so many people want to see open.”

Acknowledging that “a lot of the country does need a haircut”, he said that he is “not going to rule out” hairdressers and barbers also being able to reopen on July 4.

Later on The Andrew Marr Show, he said the Government will announce the results of a review into the two-metre rule, and the next step for the lockdown, this week.

“I think we are about to see another step in the plan and this week we will announce further details of the measures that we can take to relieve some of the national lockdown measures at the start of July including on July 4,” he said on the BBC programme.

“We’re going to set out those details absolutely this week.”

He gave perspex screens, masks and altered seating arrangements as examples of measures to mitigate the risk of spreading coronavirus if the two-metre rule is changed.

And he floated the idea that punters at pubs and bars could have to sign a guest book with their names and contact details so they could be swiftly traced if they come into contact with an infection.

Shadow health secretary Jonathan Ashworth said Labour would support a reduction of the two-metre rule “under certain circumstances”, including the strengthening of other protections such as masks.

It’s very much a matter for the Chancellor

Hotels are also awaiting the go-ahead to reopen and revive the chance of holidays within the UK and boost the economy.

To aid the recovery, Mr Hancock did not rule out suggestions that Rishi Sunak could slash VAT to encourage spending, telling Ridge: “It’s very much a matter for the Chancellor.”

The Health Secretary also said a reduction in the distance rule would “undoubtedly help with schools”, pointing to Northern Ireland where it will be reduced to one metre.

Later Boris Johnson said he is “sticking like glue” to his road map for easing the coronavirus lockdown for the hospitality sector from July 4, and confirmed he will this week unveil his plan for the future of the two-metre rule.

In a Downing Street interview, the Prime Minister said: “The disease is increasingly under control and I just want people to reflect on that important fact.

“So, of course, as we make that progress it will be possible to open up more and you will be hearing more about what we want to do with not just non-essential retail but with the hospitality sector from July 4 and we’re sticking absolutely like glue to the road map to the plan that I set out on May 10.”

A strong hint that it will also be reduced in England earlier came from Mr Sunak, who said the review ordered by Mr Johnson “will make an enormous difference” to businesses.

The Prime Minister has been under pressure from his own MPs as well as the hospitality sector to reduce it.

In other developments:

– The Scottish Government said there were no deaths of patients who had tested positive for Covid-19 in the past 24 hours, for the fifth time in June.

– Mr Hancock welcomed “hugely positive progress” in the coronavirus fight after Northern Ireland on Saturday said there had been no new confirmed cases for the first time since the lockdown was imposed.

– The Government is expected to make an announcement on the next phase of its coronavirus border controls next week after imposing a 14-day quarantine on all new entrants.

– Spain said it would “freely” welcome Britons without the need to quarantine there from Sunday, in a call for the UK to reciprocate and form a so-called air bridge.

Plans to further ease the lockdown emerged as the total number of deaths involving coronavirus in the UK is thought to have passed 53,000.