Boris Johnson is under mounting pressure to announce immediate new coronavirus lockdown measures as he acknowledged there was "no question" tougher action was needed.
The Prime Minister said he would act "in due course" and "will do everything that's necessary".
But he was warned not to delay the announcement of new restrictions in England as cases and pressure on the NHS increased.
In Scotland, Nicola Sturgeon announced the nation will go into lockdown for the rest of January with a legal requirement to stay at home and schools closed to most pupils until February.
To those arguing winter is always like this in the NHS: you are wrong. I faced four serious winter crises as Health Sec and the situation now is off-the-scale worse than any of those.
— Jeremy Hunt (@Jeremy_Hunt) January 4, 2021
Setting out the measures to come into force from Tuesday, the First Minister told MSPs in Holyrood: "It is no exaggeration to say that I am more concerned about the situation we face now than I have been at any time since March last year."
The Government hopes the arrival of the Oxford/AstraZeneca vaccine – which was injected into the first recipients on Monday as part of the national rollout – will change the course of the fight against coronavirus.
But the Prime Minister warned there would be "tough" weeks to come as cases continue to surge.
The latest data show a 41% rise in the number of confirmed coronavirus patients in hospital in England between Christmas Day and January 3, figures which have caused alarm in Whitehall and the health service.
"If you look at the numbers there's no question we will have to take tougher measures and we will be announcing those in due course," Mr Johnson said during a visit to Chase Farm Hospital in north London.
With 78% of England's population already under the toughest current restrictions, ministers are examining how successful the Tier 4 measures – which came into force for the first time on December 20 – have been.
Former health secretary Jeremy Hunt called for immediate action to close schools, shut borders and ban household mixing, saying the situation was "off-the-scale worse" than previous winter crises faced by the NHS.
"In the face of exponential growth even waiting an extra day causes many avoidable deaths so these plans must now be urgently accelerated," he said.
Senior Tory Neil O'Brien said procedures "need to toughen up at the border" in order to prevent cases being imported – a particular concern given the potential for new variants such as the one in South Africa.
The rollout of the Oxford/AstraZeneca vaccine – which is easier to distribute than the other approved jab from Pfizer/BioNTech – could provide a route out of further lockdowns, but it could be months before sufficient numbers have received their first shot.
Brian Pinker, 82, was the first person to receive the jab outside clinical trials.
Ministers have said the NHS has the capacity to deliver two million doses a week of the Oxford vaccine but supplies are limited.
While some 530,000 doses are to be available from Monday, the Department of Health and Social Care (DHSC) said tens of millions more are to be delivered in the coming weeks and months once batches have been quality checked.
Mr Johnson said: "We have the capacity, the issue is to do with supply of the vaccine.
"It's not so much a manufacturing issue although that's part of it.
"Each batch needs to be properly approved and quality controlled."
Meanwhile, uncertainty continued around the reopening of England's primary schools this week.
Mr Johnson said "the risk to kids is very, very small" and "the risk to teachers is no greater than it is to anyone else".
Education unions have urged the Government to "pause" a return to the classroom until the safety of staff and pupils can be guaranteed.
In a joint statement, the GMB, NAHT, NASUWT, NEU, Unison and Unite unions said there is a "serious risk" of staff falling ill while the rate of infection is so high.
"Bringing all pupils back into classrooms while the rate of infection is so high is exposing education sector workers to serious risk of ill-health and could fuel the pandemic," the unions said.
Shadow education secretary Kate Green said there needs to be a "stronger set" of coronavirus restrictions in place with a clear "stay at home" message to the public.
She told BBC Radio 4's Today programme: "It is very clear that the Government has lost control of the virus, we're seeing a really alarming rise in cases and in the spread of the infection."
Dr Mike Tildesley, a member of the SPI-M modelling group which advises the Government, warned that closing schools would not be enough to get the R number – the reproduction rate of the virus – below one without better public adherence to the wider restrictions.
Mr Johnson urged the public to comply with the rules in their area despite the frustration the restrictions caused.
"We will do everything we can to keep the virus under control and people should be in no doubt that the Government will do everything that's necessary," the Prime Minister said.
"But I must stress at this critical moment it is so vital that people keep disciplined."
In London, one of the first set of areas to enter Tier 4, case rates are the highest in England.
In the seven days to December 30 the rate stood at 934.3 cases per 100,000 people, up from 844.3 the previous week, and 531.5 two weeks ago.
Hospitals in the capital have a record number of patients with Covid-19, with 6,358 as of 8am on January 3, more than double the number a fortnight ago and above the first wave's peak of 5,201 on April 9.