Two-thirds of people aged between 65 and 69 have already received their first dose of a coronavirus vaccine - just a week after invitation letters were sent out.
NHS England chief executive Sir Simon Stevens said there were "early signs" that the campaign is contributing to the fall in coronavirus hospitalisations.
"The NHS Covid vaccination campaign continues full steam ahead - letters inviting everyone aged 65 to 69 went out a week ago, and already over two thirds of them have had their first Covid vaccination," he said.
"Across England overall nearly a third of adults have now had their first jab, and early signs suggest this is contributing to the welcome fall in coronavirus hospitalisation that we're now seeing."
More than 17.2 million people across the UK have now received their first dose of a vaccine, with more than 600,000 receiving their second.
Some parts of England had already begun vaccinating the over-65s in advance of invitations being sent out after offering jabs to everyone in the top four priority groups, which included the over-70s, those at very high risk of severe illness from coronavirus, frontline health workers and care home residents.
Prof Powis said: "Over 14.5 million of the most vulnerable people in England have already safely had their first dose of the Covid-19 vaccine and with people aged between 65 and 69 now eligible too, we want everyone else in this age group to consider making this week your week to get a jab.
"They can - including from later this week anyone aged 64 - use the online national booking service to book in at their nearest vaccination centre or pharmacy, so anyone that is able to do so should act this week to seize their opportunity for a life-saving vaccine."
Additional reporting by Press Association
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