Some Conservative backbenchers are pressuring for England to follow Scotland and Wales in exempting under-12s from the six-person limit from the measures to slow the spread of coronavirus.
The Cabinet Office Minister defended the restriction, to be introduced on Monday, and went further in signalling support for a proposal of fining people who refuse to self-isolate.
Asked if the Government was considering the exemption, he told BBC Breakfast: “No. I entirely understand, family life is so important, but the rule is there, the rule is clear and it commands public confidence.”
He said that the measure is necessary to “keep the reinfection rate down” so “we can protect our grandparents”.
“And then we can ensure in due course that these restrictions can be relaxed and my hope like so many is that we can have a proper Christmas,” he added.
Londoners enjoy Friday drinks ahead of new coronavirus rules
But the new rule is one of two fronts in which the Government is facing rebellion from Conservatives, with some senior Tories also wanting to derail Boris Johnson’s controversial Brexit legislation.
Tory former minister Steve Baker has called for a “voluntary system” of Covid-19 guidance so Britons can “actually start living like a free people”, while senior MP Sir Desmond Swayne said the ban was “absolutely grotesque”.
Amid allegations the Government was losing control of the virus, Mr Gove indicated support for plans being considered by the Prime Minister to enforce self-isolation guidance.
“I think it is a very fair point,” Mr Gove told BBC Radio 4’s Today programme.
“I don’t want to see fines being levied but even more I do not want to see people behaving in a way that puts the most vulnerable at risk.
“Sometimes there’s an argument that’s depicted as though this is pernicious of the liberty of freedom-loving people, well there are restrictions, and I love freedom, but the one thing I think is even more important is that you exercise freedom with responsibility.”