More than 4 million people in the UK have received their first dose of a coronavirus vaccine, according to government figures.
Speaking during a Downing Street briefing, Mr Hancock said more than half of those over 80 and half of elderly care home residents had been vaccinated.
He said that in some parts of the country the majority of people in their 80s had had their first dose.
However, Health Secretary Matt Hancock said UK data showed more people were in hospital with Covid than ever and urged people to follow lockdown rules.
He said: “Do not blow it now. We are on the route out. We have to stick at it.”