Government data shows 33,508,590 first doses have been given - the UK's estimated population is 66.7m.
More than 12 million people who are "most vulnerable to Covid" have been given both doses of the vaccine.
Mr Hancock called it "a brilliant milestone", saying "this vaccination programme is our way out" on Twitter.
"It's clearly saving lives - we can see that - and it's meaning that fewer people are catching the disease as well."
He added that he was "thrilled" the uptake among those aged over 50 was over 95% "which will give this country so much protection in the weeks and months ahead."
In England, all those aged 45 and over, as well as those who are vulnerable, are currently eligible to have the vaccine.
Saffron Cordery, deputy chief executive of NHS Providers, praised frontline NHS staff and volunteers who have administered more than 45,580,400 jabs in the UK over five months.
"We've made truly significant progress, but we've still got a long way to go until we reach our next major milestone of offering all adults their first jab by the end of July," she added.
She urged people to continue to follow the rules and maintain social distancing: "These measures are key to keeping Covid-19 infection rates under control and helping ensure this current lockdown is our last."
The latest data shows a further 32 people have died within 28 days of testing positive for coronavirus, bringing the total UK death toll to 127,417 by that measure.
Separate figures published by the UK's statistics agencies show there have been 151,000 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
A small number of "unusual infections" have been identified in patients at the Royal Aberdeen Children's Hospital.