Pregnant women will also now be able to book and will be directed to vaccination centres offering Pfizer and Moderna.
The vaccine rollout will continue to younger age groups, with the aim of giving all adults at least one dose by the end of July, NHS England confirmed.
People under 40 will instead be offered an alternative to the AstraZeneca jab, such as the Pfizer or Moderna vaccines.
As of Tuesday, 35.6 million first doses of Covid-19 vaccines have been given in the UK, with a further 18 million second doses.
Nearly three-quarters of people aged between 40 and 49 have now had their first dose, NHS England said, less than a fortnight after they were first offered a jab.
‘Protect yourself and loved ones’
NHS national medical director Professor Stephen Powis said: “The success of the NHS Covid-19 vaccination programme is not by accident but down to the careful planning and precision of NHS staff who have now delivered over 45 million first and second doses in the fastest and quickest vaccination drive in NHS history.
“We must not forget that behind the huge numbers of people jabbed, there has been a huge amount of hard work from our staff, aided by incredible volunteers across the country.
“We are incredibly grateful for their efforts.
“When you get that text, book your appointment and join the millions who have already been jabbed, protecting both yourself and your loved ones.”
‘Vaccines way out of pandemic’
Health and Social Care Secretary Matt Hancock said: “Our incredible vaccination programme has already saved thousands of lives and has helped to significantly reduce hospital and infection rates, allowing us to begin safely easing restrictions.
“Vaccines are our way out of the pandemic and I’m delighted we are now inviting people aged 38-39 to get their jabs.
“I urge everybody to get the vaccine as soon as they are eligible to protect yourself and your loved ones.”
Additional reporting by PA.