United Kingdom records 5,341 new Covid cases and four deaths
The senior Cabinet minister said the spread of the Delta variant, behind a recent rise in coronavirus infections in the country, had made the unlocking plans set for June 21 more hard. But people who have received two doses of vaccine, should be equally protected against either variant, he added.
People who cannot go online can call the booking service on 119 instead to book their jab.
Mr 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 United Kingdom by the end of next month". "That figure, around 40 per cent more transmissible, is indeed the latest advice I have", health secretary Matt Hancock told Sky News.
In Scotland, people aged 30 and over are eligible for a vaccine.
"This week we will be opening up vaccines to the under-30s and so we are getting a step closer to the point when we have been able to offer the vaccine to all adults in this country. We all need to go and get vaccinated and that way we will break this link between the number of cases and the number of hospitalisations", he added.
Matt Hancock, in what will be viewed as the clearest indication yet that the target date for lifting all restrictions could slip, stressed that June 21 was a "not before" date and that it was only "pencilled in" as the next step out of lockdown.
It comes as a surge in Covid-19 cases including the Indian variant continues to spread across the UK.
Pedestrians, some wearing a face mask or covering due to the COVID-19 pandemic, walk along Oxford Street in central London on June 6, 2021.
"Yes, I wouldn't rule that out", Mr Hancock told the BBC. "And separately we have a piece of work on what the social distancing rules should be after that", he said.
Anyone in the age groups now eligible for a vaccine is asked to book their jab once they receive the text message alert, with Global Positioning System also set to urge the newly eligible to come forward, over the coming days.
The Joint Committee on Vaccination and Immunisation (JCVI) recommended in May that the second dose interval should be reduced from 12 weeks to eight for those aged 50 and over, as well as the clinically vulnerable.
Despite the rise in cases, the number of COVID-19 deaths in Britain remains relatively low, as three-quarters of United Kingdom adults have received at least one dose of the vaccine.