Mr Hancock’s comments came as he announced that all hospital workers would have to wear surgical face masks at all times from June 15, with all hospital visitors and outpatients having to wear face coverings.
It followed the Transport Secretary announcing that face coverings would be mandatory on public transport from the same date.
The modelling has a two to three-week lag, meaning it does not take account of the latest easing of the lockdown.
The latest official ‘R’ number is 0.7-0.9, and figures from the ONS show that the number of infections in the community have more than halved in a week, but the PHE study has sparked suggestions that restrictions need to be reimposed.
Tameside council, in Greater Manchester, reacted by imposing its own lockdown, telling its schools they were “strongly advised” not to reopen after the PHE modelling estimated the ‘R’ value in the north-west at 1.01.
It put back the recommended reopening date to June 22, while nearby Bury council wrote to headteachers saying they “may wish to reconsider” opening on Monday.
The councils also asked people to stay at home over the weekend. Other councils in the area were holding meetings on Friday to decide whether to follow suit.
Mr Hancock recommended that people consider evidence on the ‘R’ value “in the round”, saying that nationally it remained below one and that, while the south-west had a higher ‘R’ value than other areas, the overall incidence of the disease was much lower.
He urged people to exercise caution this weekend and follow the rules banning gatherings of more than six people from different households.
And he asked people not to gather in large groups for protests against the killing of George Floyd in the US , saying he was “appalled” by his death but people needed to stick to the rules to “protect themselves and their families”.