Coronavirus vaccines will be offered to those aged 36 and over from Tuesday.
The latest move was confirmed by health secretary Matt Hancock during an announcement in the House of Commons on Monday.
Texts inviting people to book a vaccination will be sent to those aged 37 on May 18, and to 36-year-olds on May 19.
The news comes against a backdrop of a surge in cases of a more transmissable Indian variant of the virus.
Mr Hancock told MPs the UK had the highest vaccination enthusiasm in the world.
He said the approach so far had saved around 12,000 lives and prevented 32,000 people from being hospitalised.
Mr Hancock said there were now fewer than 1,000 people in hospital and the average daily number of deaths was now nine.
However, he urged people to get their vaccine as soon as possible.
Priority will be given to second jabs for under-50s and first jabs for those over 50 who have been hesitant.
Mr Hancock confirmed there were 2,323 cases of the Indian variant in the UK, adding the majority in hospital were those who had not yet had the chance to have, or who had refused the vaccine.
Official government figures for Lincolnshire, released on Thursday, showed that more than 71.3% of residents had had their first jab and 36.1% their second.
Altogether 676,851 jabs have taken place in the county between December 8 and May 9 — a further 42,145 in the previous seven days, and nearly 10% up on the 38,553 jabs given the week before.