About one million people aged 30 and 31 will get a text message in coming days asking them to come forward for their Covid vaccine.
Health officials have sped up the timetable to offer second jabs in a bid to ensure that those at highest risk are protected from the variant of the virus first identified in India.
At the same time, the programmes are extending to younger age groups to try and mitigate risk.
Mr Hancock said: “Our vaccination programme is moving at such a phenomenal pace and I am delighted that less than six months after Margaret Keenan received the first authorised jab in the world, we are now able to open the offer to everyone in their 30s and over.
“The vaccine is our way out of this pandemic and recent data has shown the life-saving protection (that) a second dose of the jab can give, especially against the new variant.
“I urge everyone to come forward when you get the offer and play a part in getting us back to normality.”
GP and national medical director for primary care for the NHS in England, Dr Nikki Kanani, said: “Getting the vaccine is the single most important step we can take to protect ourselves, our families and our communities against Covid-19 with the jabs saving thousands of lives already.
“The offer of a vaccine doesn’t expire so, if you are eligible and haven’t booked, please do come forward when you’re invited to.”
Vaccination experts have previously advised that people under the age of 40 should receive an alternative vaccine to the Oxford/AstraZeneca jab due to the link between the jab and extremely rare cases of blood clots.
This means that most under-40s will be offered the Pfizer or Moderna vaccines.
NHS leaders in Scotland are encouraging people aged 30 and over to come forward for their jab and in Northern Ireland, those aged 25 and over are eligible for the vaccine.
In Wales the invite is open to all people over the age of 18.
It comes after the Government said on Tuesday it would be updating guidance to make it clear that lockdown measures are not being imposed for eight areas considered to be hotspots for the Indian variant of coronavirus in England.
The Department of Health and Social Care said it would instead be issuing advice to people living in Burnley, Bedford, Blackburn with Darwen, Bolton, Kirklees, Leicester, Hounslow and North Tyneside after ministers were accused of bringing in rules on socialising and travelling “by stealth”.
The advice, which the Government said is not new regulations, will highlight “additional precautions” residents can take, such as meeting others outdoors rather than indoors, staying two metres apart from people not in the same household, and minimising travel in and out of the area.
The move follows a day of confusion over the measures which appeared on the Government website on Friday, but without an official announcement and local leaders being made aware of any change.