Hancock said there had been a "very significant" impact from the delta variant of Covid-19 first detected in India over the last month, which is now the dominant strain in England, according to official estimates. "That means that it is more hard to manage this virus with the new Delta variant, but crucially we believe that with two doses of the vaccine you get the same protection as the old variant".
The UK faces a "moral and ethical balance" on prioritising the country's children or the wider world when it comes to vaccination, Professor Calum Semple, a member of the Scientific Advisory Group for Emergencies (Sage), has said.
"We are not saying "No" to June 21 at this point", he added. "We'll look at the data for another week and then make a judgement", he told the BBC on Sunday, stressing that the government was "absolutely open" to delaying the lifting of restrictions.
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.
Mr Hancock said he expected "around three fifths" of all adults to have been fully-vaccinated by June 21, with 52% now double-jabbed, as indicators suggest vaccines are helping to cut the link between case rises and an increase in hospital admissions.
"We all need to go and get vaccinated and that way we will break this link between the number of cases to the number of hospitalisations".
He said: "The majority of people going into hospital right now are unvaccinated".
Shadow education secretary Kate Green told Trevor Phillips on Sunday the decision on whether or not to ease restrictions on June 21 needs to be "transparently taken" and "robust".
The president of the Academy of Medical Sciences Dame Anne Johnson said next week will be "absolutely critical" in looking at data on infections.