Mr Hancock said ministers would be publishing clear guidance on close personal contact.
“It depends on people’s circumstances. We will be changing the rules to be far more about people taking personal responsibility, exercising common sense according to their circumstances,” he told Sky News.
“We will set out really clearly the risks. People understand the risks – we know that – and we’ll make that very, very plain and then people can exercise their own personal responsibility.”
He added: “Grandparents, sometimes for the first time in over a year, will be able to be close to their grandchildren, but taking into account the individual risk of catching this disease which differs according to circumstances.”
He told BBC Breakfast this morning: “There is no doubt that a new variant is the biggest risk. We have this variant that was first seen in India – the so-called Indian variant – we have seen that grow.
“We are putting a lot of resources into tackling it to make sure everybody who gets that particular variant gets extra support and intervention to make sure that it isn’t passed on.
“However, there is also, thankfully, no evidence that the vaccine doesn’t work against it.”
Scientists say that in England, in the two weeks to May 1, the proportion of Indian variant cases went from one per cent to 11 per cent of Covid-19 infections, with other variants less than one per cent.
It comes as the World Health Organisation (WHO) classified the variant as “of global concern”.
The WHO said as it confirmed the variant has spread to more than 30 countries.
Three other variants from Kent, South Africa and Brazil have been given the same designation.
The Indian government says there is evidence of a link between the variant and India’s deadly second wave, but that the correlation is not yet “fully established”.
Additional reporting by the Press Association.