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.