The reproduction "R" number, which measures transmission rates, has dropped below 1.0 for the first time since July.
Britain's speedy roll out of vaccines could also help convince the government to lift lockdown measures, although there are concerns about the effectiveness of the vaccine on new variants of the virus.
More than 13 million people have had a first shot of the vaccine.
During a visit to a vaccination center in Alyesbury on Friday, Hancock said "we're on track to have met the target by Monday to offer everyone who's over 70 health and social care worker or clinically extremely vulnerable to offer them a vaccine."
England has been in lockdown since January 5, with schools shut for most children.
Government ministers have said that any easing of restrictions will depend on data over the coming weeks, with an announcement expected on February 22.
- It's clearly good news that the number of cases is coming down. The plan is working, but we're a long way off getting this sorted. There's still over 25,000 people in hospital with coronavirus right now. So everyone can have confidence that the plan is working. What we're collectively doing together is having a really positive impact, but there's still a long way to go. We're on track to have meet the target by Monday to offer everyone who's over 70, a health and social care worker, or clinically extremely vulnerable to offer them a vaccine by Monday. We're in the final push and-- I know an elbow--