In a televised address on Monday, Boris Johnson announced stringent new controls, including closing schools to most pupils, in an attempt to prevent the NHS being overwhelmed by a surge in new infections.
At the same time, the Prime Minister raised the prospect the vaccination programme being rolled out across the country could enable restrictions to be progressively eased from mid-February.
But, in a round of broadcast interviews on Tuesday morning, Mr Gove said relaxation of the rules may have to wait until the following month – and that even then some measures may have to remain in place.
"We will keep these constantly under review, but we can't predict with certainty that we will be able to lift restrictions in the week commencing February 15-22," he told Sky News.
"What we will be doing is everything that we can to make sure that as many people as possible are vaccinated, so that we can begin to progressively lift restrictions.
"I think it is right to say that, as we enter March, we should be able to lift some of these restrictions, but not necessarily all."
Chancellor Rishi Sunak, meanwhile, unveiled a fresh £4.6 billion support package for businesses dealt a further crippling blow by enforced closures.
It includes one-off top-up grants worth up to £9,000 for firms in the retail, hospitality and leisure sectors to help nurse them through to the spring.
Mr Johnson's announcement came after First Minister Nicola Sturgeon imposed a lockdown on Scotland for the rest of January, with a legal requirement to stay at home and schools closed to most pupils until February.
Schools and colleges in Wales will also remain closed until at least January 18 and move to online learning, while in Northern Ireland, which is already under a six-week lockdown, "stay at home" restrictions will be brought back into law and a period of remote learning for schoolchildren will be extended.
In his address, Mr Johnson warned the coming weeks will be the "hardest yet", but said "with a fair wind in our sails" it should be possible to vaccinate 13 million of the most vulnerable people by mid-February, paving the way for controls to be eased.
The Prime Minister had previously strongly resisted calls to delay the reopening of primary schools in particular following the Christmas break - despite pressure from the teaching unions.
Mr Gove said they had been forced to act with a "heavy heart" after the chief medical officers of the four nations warned there was a danger the NHS would be overwhelmed by the surge in infections caused by the new variant of Covid-19.
"In the circumstances we felt that the only thing we could do was to close those primary schools that were open," he said.
With the UK Government acknowledging that exams will not be able to go ahead as planned in the summer, Education Secretary Gavin Williamson will address a recalled House of Commons on Wednesday to update MPs on how pupils will be assessed.