The cabinet minister said Boris Johnson would announce on Monday that the lifting of restrictions on indoor mixing will proceed as set out on the government’s roadmap.
It means restaurants and pubs will be free to reopen indoors, museums and hotels can reopen, and performances and sports can resume with caps on audience numbers.
Mr Gove also indicated that “friendly contact” such as hugging can resume between friends and family, who will be allowed to meet indoors in groups of six and outdoors in groups of 30.
Mr Gove told Sky News’s Sophy Ridge: “I’m genuinely worried, as everyone should be, about incidents of variants of concern, but there’s no indication at the moment that it need slow down the relaxation that we have as part of the roadmap.
“I anticipate that the prime minister tomorrow will signal that we can enter into the next stage of relaxation in England.”
The India variant, or B16172, was declared a variant of concern by Public Health England on Friday. Officials said that cases of this variant more than doubled, from 202 to 520, in the country over the last week.
But the body added that there is currently “insufficient evidence” to suggest that it causes more severe illness or makes Covid-19 vaccines any less effective.
Mr Gove said “friendly contact” between friends and family will be allowed from 17 May, but added that social distancing recommendations will remain in place elsewhere.
He told the BBC’s Andrew Marr: “It will be the case that we will see people capable of meeting indoors and, without prejudice to a broader view of social distancing, it is also the case that friendly contact, intimate contact, between friends and family is something we want to see restored.”
Asked about hugging, the head of the Oxford University vaccine group Professor Andrew Pollard told Mr Marr that was time to start relaxing such restrictions.
He said: “I think it is time to start, based on the very careful modelling that’s been done, relaxing some of those restrictions,” adding that “we’re in a very fortunate position here in the UK”.
From 17 May, up to six people or two households will be allowed to meet indoors, while groups of under 30 will be allowed to gather outside.
Pubs, cafés and restaurants can to seat people inside, while hotels, hostels, B&Bs, cinemas and children’s play areas will be allowed to reopen.
Performances and sporting events can take place in and outdoors, as long as the seats are only half full. There is a cap of 1,000 people inside and 4,000 people outside, although up to 10,000 people can attend events at very large outdoor venues where social distancing is possible.
The government has already announced that some international travel for leisure can resume from 17 May.
However, only 12 destinations are currently on the government’s green list, such as Portugal and Israel, and not all of them are accepting foreign visitors.