People aged between 56 and 59 are being invited to book Covid-19 vaccinations this week, NHS England has said.

Hundreds of thousands of letters for the age group began landing on doorsteps on Saturday; the latest round of invites comes after eight in 10 people aged 65-69 took up the offer of a jab, it added.

More than 18 million people across England – more than one-third of the adult population – have already received a vaccine. Across the whole of the UK, more than a million people have received both doses of a Covid-19 vaccine, while almost 21.4 million people have had one dose.

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 is eligible but hasn’t been vaccinated yet, I’d urge them to go online or call 119 and get themselves booked in.”

The health secretary, Matt Hancock, said more than nine in 10 of those aged 65 and over and nearly nine in 10 people who are clinically extremely vulnerable have received a first dose. A first jab would be offered to all adults by 31 July, he added.

“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,” Hancock said.

NHS England said: “Vaccinations are now being administered at more than 1,600 sites across the country, including mosques, museums and rugby grounds, with the distribution of centres meaning 98% of the country lives within 10 miles of at least one vaccination service.

“People can use the national booking service to reserve a slot at a NHS vaccination centre or one of the pharmacy-led services across the country.”

A total of 19,258,271 Covid-19 vaccinations have now taken place in England between 8 December and 5 March, according to provisional NHS England data, including first and second doses, which is a rise of 422,916 on the previous day’s figures.

Of this number, 18,491,771 were the first dose of a vaccine – a rise of 385,681 on the previous day, while 766,500 were a second dose – an increase of 37,235.

NHS England data shows that a total of 2,333,627 jabs were given to people in London between 8 December and 5 March, including 2,229,397 first doses and 104,230 second doses. This compares with 3,603,903 first doses and 134,215 second doses given to people in the Midlands, a total of 3,738,118.

The NHS was the first health system to deliver the Oxford/AstraZeneca coronavirus vaccine when Brian Pinker, 82, received his on 4 January. Meanwhile, Piers Morgan on Saturday became the latest public figure to get the jab.