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The country, which was the first to approve vaccines developed by Pfizer-BioNTech and by Oxford-AstraZeneca, is currently immunising about 200,000 people a day, Health Secretary Matt Hancock said on Sunday.
It needs to boost that rate to 2 million a week to meet its target of vaccinating those in care homes, the over-70s, the clinically vulnerable with pre-existing conditions and health and social-care workers by February 15.
Britain is battling surging infections but is pinning its hopes on rapid immunisation to enable life to start returning to some degree of normality by the spring.
Health Secretary Matt Hancock will set out his Covid-19 immunisation plan - the biggest vaccination programme in British history - later on Monday.
"The UK vaccine delivery plan will be the keystone of our exit out of the pandemic, but we all must continue to play our part by staying at home, following the rules and keeping hands, face, space at the forefront of our minds when out and about," he said in a statement.
More than 81,000 people in Britain have died within 28 days of receiving a positive Covid-19 test, the fifth-highest official death toll globally, and over 3 million people have tested positive.
The centres include London's Nightingale field hospital, a soccer stadium in Bristol in the west, Epsom racecourse in the southeast and a tennis club in Manchester in the north, the government said.
Hundreds of additional doctors' surgeries and hospitals and some pharmacies will also start delivering shots this week, taking the total number of sites to 1200, the government said.