Health Secretary Matt Hancock has issued a renewed appeal for people to get the coronavirus jab amid warnings that the virus may persist in deprived inner city communities where uptake is low.

After Prime Minister Boris Johnson set out his “road map” out of lockdown in England – with a gradual lifting of restrictions over the coming months – Mr Hancock said it is “absolutely on all of us” to get the vaccination when invited.

The Government has faced criticism from some Tory MPs over the pace of the easing, which will not see all legal controls removed until June 21 at the earliest.

Chairman of the Covid Recovery Group Mark Harper said that, with uptake of more than 90% among those groups which have been offered the vaccine, the country should not be “held back” by those who refuse it.

However, Dr Mike Tildesley, reader in mathematical modelling of infectious diseases at the University of Warwick and member of government advisory group SPI-M, warned that failure to ensure all communities are protected could lead to a new wave of infections.

“We know there are certain areas –  in particularly inner city areas, deprived areas – where vaccine uptake is not as high,” he told BBC Radio 4’s Today programme.

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“And that actually poses a real risk that we are not capturing currently in those models – if we do get these pockets of infection then it could be that actually we could have a more significant risk.

“So actually it’s really important that we get the vaccines out to those deprived communities to prevent a potential wave of infections occurring as we do unlock.”

He added: “This is a real concern … that we may end up in a situation where we have the ‘vaccine rich’, as it were, who are able to access the vaccine, who have taken up the vaccine and are at much lower risk, and maybe the people in society who have not taken up the vaccine.

“Potentially these individuals could be clustered in particular parts of the country, and there is increased risk there.”

Mr Hancock said the Government is working “incredibly hard” to ensure as many people as possible receive the vaccine.

“We want to see that vaccine uptake go as high as possible. But it’s absolutely on all of us to come forward and get the vaccine. It’s the right thing to do,” he told the Today programme.

However, Mr Harper accused ministers of basing their plans for easing restrictions on “dodgy assumptions” about the rate of uptake, which is actually significantly higher than had been expected.

He said it means the relaxation could be brought forward, two months earlier than is currently planned.

“The biggest flaw is they assume a very low uptake of the vaccine,” he told LBC.

“We know the uptake of the vaccine is over 90% in the top groups that have been vaccinated, above 95%, they’ve assumed 15% of the population don’t take the vaccine.

“I have two problems with that; one is that isn’t realistic, that’s not what’s happening, but secondly there is a real question about whether the rest of the country should be held back for two months because some people choose not to take the vaccine.”

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Setting out his four-step plan on Monday, the Prime Minister defended his “cautious but also irreversible” approach to relaxing restrictions, saying he would not be “buccaneering” with people’s lives.

Despite billing it as a “one-way road to freedom”, he admitted, however, he could not guarantee that the vaccination programme will prevent restrictions from ever returning.

His tentative schedule for easing restrictions will be followed on Tuesday afternoon by First Minister Nicola Sturgeon detailing her own plan for easing Scotland’s lockdown.

Mr Johnson accepted that scientific modelling suggested that lifting measures will increase Covid-19 cases and ultimately deaths, but said restrictions cannot continue indefinitely.

In the first step of the “road map”, all pupils in England’s schools are expected to return to class from March 8, with wider use of face masks and testing in secondaries.

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Socialising in parks and public spaces with one other person will also be permitted from that date.

A further easing will take place on March 29, when the school Easter holidays begin, with larger groups of up to six people or two households allowed to gather in parks and gardens.

But progressing along the schedule will depend on meeting four tests: the success of the vaccine rollout, evidence of vaccine efficacy, an assessment of new variants, and keeping infection rates below a level that could put unsustainable pressure on the NHS.

In Scotland and Wales the phased return of children to classes began on Monday, with Welsh First Minister Mark Drakeford suggesting stay-at-home orders could be eased in around three weeks.

In Northern Ireland, First Minister Arlene Foster has promised a “decision-making framework” on how the executive plans to exit lockdown will be published on March 1.