Around three million more people across the country will become eligible to book their first dose as Matt Hancock said that people aged 25 to 29 will be invited to book their jab from tomorrow (June 8) onwards.
Alongside opening up appointments to younger age groups, the NHS is pressing ahead with offering second doses to people at pace.
The so-called race between variants and vaccines has led to a sped-up timetable for offering second jabs.
Instead of waiting 12 weeks for their second dose, people are now being invited back after eight weeks.
It comes amid concerns over the spread of the variant first identified in India, known as the Delta variant.
Only a handful of people have been admitted to hospital after having both doses of the vaccine, NHS leaders have said previously.
Hancock told MPs: “From this week we will start offering vaccinations to people under 30, bringing us ever closer to the goal of offering a vaccine to all adults in the UK by the end of next month.
“From tomorrow morning we will open up vaccination to people aged 25-29. Over the remainder of this week the NHS will send texts to people in these age groups and of course GPs will be inviting people on their lists to come forward.”
NHS England chief executive Sir Simon Stevens said: “Today is a watershed moment as the world-beating NHS vaccination programme enters the home straight of our race to offer everyone their first dose.
“The NHS vaccination programme is a real team effort and it is a testament to NHS teams across the country that we are able to open up to people in their 20s just six months on from delivering that world-first jab to Maggie Keenan.
“The tireless efforts of NHS staff to protect the people they care for and their communities has quite simply saved lives, and when you get the text, you’re next.
“Getting the lifesaving Covid-19 jab is the most important thing you can do, with NHS staff vaccinating at over 1,600 sites, including vaccine buses, places of worship, sport stadiums and other convenient locations. So when you get that text, book your appointment and join the millions who are already protected.”
In Peterborough, as of May 30, a total of 104,274 vaccines had been administered since the beginning of the programme. This is approximately 54% of the local authority population.
More than 14,300 of the most recent age bracket to be called - those in their 30s - have received their first jab. With a population of around 43,000, this means that around 33% of people between the ages of 30 and 39 have received a Covid vaccine.
Approximately 64% of residents in their 40s have been given their first dose, alongside 79% of residents in their 50s and 85% of those in their 60s.
All of these are slight rises on last week's figures, but still only two age brackets in Peterborough have more than 90% takeup - those aged over 70 and those over 80.
Second doses in Peterborough total 64,969, meaning 62% of people who have accepted their first vaccine appointments have now been fully inoculated against Covid-19. This is a third (33%) of the whole local authority population.
This is mostly adults over the age of 50, with younger age groups yet to reach the recommended 12 weeks since their first jab.