Boris Johnson faces demands to vaccinate all adults in areas where Covid-19 cases are rising.
The Indian variant is blamed for a spike in cases in Bolton, London, Glasgow and Bedford.
As fears of a summer of restrictions grew, Shadow Health Secretary Jonathan Ashworth called for a “surge vaccination” campaign.
Mr Ashworth said: “Some alarm bells need to start ringing. We’re not out of woods yet. We need to contain this variant, fast
“So called ‘surge vaccination’ should be considered.
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“We can break transmission with retrospective & forward contact tracing.
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Cases across the UK of the Indian variant have shot up from 520 last week, to 1,313 cases in the past seven days.
The case rate per 100,000 people in Bedford has more than doubled to 84.3 from 39.8 in just one week and the rise in cases is mostly among people aged under 40.
Bedford mayor Dave Hodgson said: “We need a vaccination programme to be rolled out for all residents aged 16 and over in the Borough to protect our residents, especially in light of some lockdown restrictions being lifted from Monday 17th May.
“We also consider it vital that a vaccine for children under 16 should be licenced as soon as possible.”
Andy Burham also tweeted saying he would have serious reservations about regional lockdowns and said: “Surely surge vaccinations for people of all ages is the best answer?”
Prof. Azeem Majeed, Professor of Primary Care & Public Health, and Head of the Department of Primary Care & Public Health at Imperial College London, tweeted: “It’s time to consider a “’surge vaccination’ campaign and enhanced ‘test and trace’ in areas of England that are seeing a rapid rise in Covid-19 cases triggered by the ‘India Variant’.
It’s essential to contain these outbreaks and prevent their spread to other parts of England.
Bolton Councillor Elaine Sherrington said: “I think vaccination is the answer to it all and I think the more people we can get vaccinated the better.
“This virus is not going to go away – we have to live with it. But if we have got the capacity to vaccinate the younger people without putting anyone else at risk then we should do it.
“I know there are 18 and 19-year-olds who have had the virus who have been very poorly.”