Boris Johnson said the government will be "looking at the potential of relaxing some measures" before the middle of next month.
Speaking at a Covid-19 vaccination site at Barnet Football Club in north London, the PM said: "We're looking at the data as it comes in, we're looking at the rates of infection, as you know the JCVI [Joint Committee on Vaccination and Immunisation] groups 1 to 4 [on the priority list] will be vaccinated by February 15. Before then we'll be looking at the potential of relaxing some measures. But don't forget this country has made huge progress in reducing infection, I don't think people want to see another big surge in infection."
A Number 10 source told Sky News the PM meant the "looking at" restrictions will happen before the middle of next month, not the relaxing of measures.
Health Secretary Matt Hancock said at the weekend that any easing was a "long, long, way off".
Mr Johnson also said ministers were "definitely looking at" requiring travellers arriving into the UK to quarantine in hotels. He said: "We have to realise there is at least the theoretical risk of a new variant that is a vaccine-busting variant coming in, we've got to be able to keep that under control."
Mr Johnson added: "We want to make sure that we protect our population, protect this country against reinfection from abroad. That idea of looking at hotels is certainly one thing we're actively now working on. We need a solution that gives us the maximum possible protection against reinfection from abroad."
Last week, the government closed all UK travel corridors - which had allowed arrivals from some countries to avoid having to quarantine - until at least 15 February.
People coming to the UK from abroad also now have to show proof of a negative COVID test from up to 72 hours before their journey.
But the PM is reportedly under pressure from some members of his cabinet to go further and follow the examples of countries like Australia and New Zealand, which have mandatory quarantines.
The PM declined to guarantee that all pupils will be back at school before Easter, but promised to tell parents and teachers "as much as we can as soon as we can. Daily we're looking at the data and trying to work out when we're going to be able to lift restrictions," he said. Schools obviously will be a priority but I don't think anybody would want to see the restrictions lifted so quickly while the rate of infection is still very high so as to lead to another great spread of infection."
Alan McGuinness, political reporter Sky News
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