UK Prime Minister Boris Johnson has insisted England will be able to fully reopen its economy and society in July.

"We are very confident that we'll be able to go through with step four of the road map, on the timetable that I've set out with treating July 19, as I've said, as a terminus date," Johnson said.

His comments came despite the latest figures from Public Health England showing cases of the Delta variant have increased 78 percent in the past week.

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The number of people with COVID-19 in hospital has almost doubled in a week, although they are thought to mostly be people who haven't been vaccinated or only partly vaccinated.

Several senior scientific advisers in the UK now believe the country is at the start of a third wave of infections. 

This includes Neil Ferguson from Imperial College London, who provided the modeling during the first wave of the pandemic that helped prompt the UK's first lockdown.

Meanwhile, everyone aged over 18 in England can now book a vaccine.

Johnson urged young people to get the jab and he thanked them for their patience.

"You've acted selflessly and sacrificed so much to save others in this pandemic. Now the end is in sight. Please get your jabs as soon as you can," he said in a message posted via social media.

The government hopes this weekend will be a "super-Saturday and Sunday" for vaccinations, with large numbers of young people going for the jab at centers set up in three of London's large football stadiums.

The prime minister has also said he supports UK Health Secretary Matt Hancock, after leaked phone messages included one that suggested Johnson thought Hancock was "hopeless."

"I have complete confidence in Matt, and indeed all of the government who've been dealing with COVID-19 throughout the pandemic," Johnson said.