Invitation letters were sent out by the NHS this weekend for the latest stage of the rollout in a bid to meet the target of offering a first dose to all adults by 31 July.
Nearly 18.5 million people - over one third of the adult population - have already received a jab in England.
That figure includes nine in 10 of those aged 65 and over and nearly nine in 10 people who are clinically extremely vulnerable.
Around eight in ten people aged 65-69 have already taken up the offer of a jab and the programme was extended to those aged between 60 and 64 last week.
Across the UK as a whole, the number of first doses is now approaching 22 million.
Dr Nikki Kanani, NHS England national medical director for primary care, said: "The NHS vaccine programme is committed to protecting the country against coronavirus and it is testament to our incredible staff that we can now move on to the next age group.
"We must not forget that our success in vaccinating more than 18 million people is down to careful planning and the hard work of those staff.
"The vaccines are both safe and effective, so if anybody who is eligible but hasn't been vaccinated yet, I'd urge them to go online or call 119 and get themselves booked in."
Health Secretary Matt Hancock said the UK "remains on track" to offer a first vaccine all adults by the end of july.
He said: "We are now inviting people aged 56 to 59 to get their jabs and I urge everyone eligible to come forward as soon as possible."
The government has decided that once the over-50s have been vaccinated, the rollout will move on to those aged between 40 and 49 rather than prioritising occupations such as teachers and police officers.
NHS England said that vaccinations are being provided at more than 1,600 locations distributed across the country so that 98 per cent of the population lives within 10 miles of a site. Booking slots can be reserved using the national service online via the NHS website.
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