Pubs and restaurants in local lockdown areas are already closing at 10pm, and the measure could be rolled out more widely amid fears that people tend not to adhere to social distancing rules when they consume more alcohol.
The proposal would affect greater numbers of young people, who have been blamed for a recent spike in infections (see graphic below showing the rising rate of infections in younger age groups).
A senior Government source said: "A national curfew is the obvious next step if the numbers keep rising despite all the steps we are currently taking.
"But we are not at that stage at the moment, and hopefully the action we are taking locally to contain outbreaks where they occur will mean we don't have to go that far."
Robert Buckland, the Justice Secretary, suggested curfews could be needed because young people "getting together and enjoying themselves" were forgetting social distancing rules.
Mr Buckland admitted there was "an issue about social occasions" and said the Government would be prepared to move "quickly where necessary".
He said: "I do think that what we're doing now is being clear about prioritising schools, colleges in the economy and making the point that while social occasions are important – and of course family social occasions are particularly important – they do take and they must take second place to those priorities."
The Justice Secretary told Sky's Sophy Ridge on Sunday that another national lockdown would be a "nuclear option", comparing the UK's fight against coronavirus to a marathon. He said the country was now at the point "where the gradient starts to go up, it feels really tough – you have to dig in".
It came as Professor Peter Openshaw warned that, if the UK does not go "back to some degree of lockdown", it will be plunged into a "hard lockdown in short order".
Coronavirus cases increased by 3,330 on Sunday and Prof Openshaw, who sits on the the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), said detection systems have "picked up this signal that we're seeing a really sharp rise in cases".
The immunologist, from Imperial College London, said: "I think everyone is in agreement that we really need to act very quickly now in order to prevent this from growing exponentially.
"I think that the main point is that we must act fast because it's so much harder to get this sort of thing under control if you delay – even a few days is potentially going to be quite dangerous."
Prof Openshaw described the "rule of six" (seen being announced by Boris Johnson in the video below), which comes into force on Monday, as "somewhat irrational" and admitted it would "cause pain and suffering".
He said: "I think people have been complaining widely about the fact that you can carry on doing things like exercising in groups and doing sports and getting together for special events, yet you can't have both a grandmother and a grandfather come to visit your home if you're a family of five.
"It is inevitably going to create those difficulties which are hard to explain. I'm afraid it's going to cause pain and suffering for us all to go back to some degree of lockdown, but I'm afraid if we don't do this now we're going to be right back in hard lockdown."
The controversial new restriction means those who gather in groups of more than six are liable to receive £100 fines.
Sir Graham Brady, the chairman of the 1922 Committee of Tory backbenchers, said he feared the measure were "a big infringement of people's liberties and their right to a normal family life".
He told Times Radio: "I'm not particularly inclined to this kind of arbitrary direction. I prefer to think the Government is there to serve us, not to tell us what to do. But the most shocking thing in this is it's simply being done on the stroke of a pen by ministers. There was perfectly adequate time for this to be debated in Parliament and voted on in Parliament."
Sir Graham said he thought children should be excluded from the rule, saying younger children were "less likely to spread the virus".