The new target date was revealed in chaotic circumstances, included apparently inadvertently in a separate announcement on the timing of local elections and initially described as an “error” by Downing Street before being confirmed.
Under the plan, more than half of UK adults should receive the jab by May, as the government completes the top nine priority groups identified by the Joint Committee on Vaccination and Immunisation.
Including all those aged 50 and over as well as health and care workers and adults with certain underlying health conditions, the nine groups comprise around 32m of the UK’s 52.7m over-18s.
Confirmation of the date led to immediate calls from Conservative MPs for an acceleration in the programme of relaxing England’s national lockdown.
Mark Harper, chairman of the Covid Recovery Group of lockdown-sceptic Tory MPs, said it would be “almost impossible to justify having any restrictions in place” once the over-50s had been vaccinated.
And Foreign Office minister James Cleverly confirmed that the government was working with other countries to “help facilitate” the production of any documentation needed to provide proof of vaccination required by destinations.
Greece has offered to waive travel bans for Britons able to provide a “vaccine passport” of this kind.
But Mr Hancock cautioned that the NHS remains under considerable pressure, with 31,670 people still in hospital with Covid-19.
“My plan is that we should be able to offer a vaccine to everybody in categories one to nine – that’s all the over 50s – by May,” said Mr Hancock.
“Lots of things have got to go right to hit that goal, especially in supply, which is the main limiting factor.
“But I’m sure that working with the NHS and everybody else who’s making this happen, if we keep going at the pace we can, then we can make sure all the over-50s get the offer of a vaccine by May.”
Mr Hancock’s comment appeared to suggest that the new target date is the start of May, as did the Cabinet Office press release which mentioned the completion of the next stage of the vaccination programme in the context of clearing the way for English local elections on 6 May.
But the Department of Health was unable to confirm the precise target date, which is due to be unveiled by Boris Johnson on 15 February.
Mr Hancock said the UK was “on track” to reach all over-70s by that deadline, as the latest daily statistics showed that almost 11m people – around one-sixth of the UK population – have now had their first jab.
Of the 10,971,047 to receive a first dose of vaccine, some 505,993 have also had a booster second inoculation.
Official figures showed that the crucial reproduction rate of the virus – known as R – has dropped to between 0.7 and 1, meaning that every 10 people with the disease will pass it on to 7-10 others.
Numbers of coronavirus deaths reported on Friday rose to 1,014, up 99 on the previous day. But the seven-day total of 6,893 was down almost 18 per cent on the week before.
There were 19,114 new cases of Covid-19 reported, with the seven-day total of 138,760 down 26.5 per cent from the previous week.
Downing Street refused to confirm reports that outdoor sports and social mixing were being considered for swift return following the planned reopening of schools to all pupils on 8 March.
A No 10 spokesman said only that these issues – as well as the question of whether pubs will be required to serve “substantial meals” along with drinks – would be considered ahead of the prime minister’s announcement of England’s roadmap to recovery on 22 February.
Mr Hancock said it was “to early to say” how the emergence from lockdown would roll out.
“Even though the vaccine programme is going great guns and almost 11 million people now have been vaccinated, 31,670 people are in hospital with Covid right now,” he said.
“That is far, far too many. So the NHS is still under pressure, and we’ve all got to do our best to keep those case rates going down.”
Scientists advising the government have warned against opening up too quickly.
Professor Graham Medley, chairman of the Scientific Pandemic Influenza Group on Modelling (Spi-M), said ministers should “make decisions dependent on the circumstances, rather than being driven by a calendar of wanting to do things”.
Mr Hancock confirmed that the government has no plans to issue vaccine passports “at the moment”.
But Mr Cleverly confirmed that officials are in discussions with other countries with a view to ensuring that UK nationals are able to comply with whatever requirements for proof of vaccination they will face in order to be able to go on holiday.
“It is often the case that the entry requirements for countries are for vaccines or inoculations, and that is not an uncommon practice,” said the Foreign Office minister.
“We will work with international partners to help facilitate their border arrangements and their immigration arrangements.”