Matt Hancock has said England is ‘clearly on track’ to further ease the lockdown.
Acknowledging that ‘a lot of the country does need a haircut’, Mr Hancock told Sky's Sophy Ridge on Sunday that he is ‘not going to rule out’ hairdressers and barbers also being able to reopen on July 4.
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 relaxed.
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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.
Boris Johnson is set to lay out the next steps in the easing of the coronavirus lockdown on Tuesday.
The Prime Minister and his most senior ministers will on Monday discuss the next steps for the lockdown with chief scientific adviser Sir Patrick Vallance and chief medical officer for England Professor Chris Whitty.
Mr Johnson will then on Tuesday outline the plans to Parliament for pubs, restaurants, hotels and hairdressers to reopen in England from July 4, and a likely loosening of the distance rule to aid the restart to the economy.
Guidance will be published for each sector on how businesses can reduce the spread of Covid-19 when they reopen.
And the public are expected to be warned that the newest relaxation of rules will be the first to be reversed if there are widespread breaches that prompt the virus to spread uncontrollably.
A No 10 spokesman said: ‘The reason we are able to move forward this week is because the vast majority of people have taken steps to contain the virus.
‘The more we open up, the more important it is that everyone follows the social-distancing rules.
‘We will not hesitate to put the handbrake on to stop the virus running out of control.’