Boris Johnson urged people to stick to coronavirus rules at a "critical moment" as his senior scientists warned hospital admissions are rising and Covid-19 is not under control.
The Prime Minister said no matter how "fed up" people are of the restrictions being imposed, they were the only way to curb the spread of the virus.
He used a Downing Street press conference to demonstrate "forbearance, common sense and a willingness to make sacrifices for the safety of others".
He warned that if the evidence required it, "we will not hesitate to take further measures" that would "be more costly than the ones we have put into effect now".
"But if we put in the work together now, then we give ourselves the best possible chance of avoiding that outcome and avoiding further measures," Mr Johnson said.
England's chief medical officer Professor Chris Whitty said there was a "long winter ahead of us" and suggested things could change rapidly.
The number of people in hospital is rising, particularly in hotspots, although the figures are at a much lower level than the beginning of April.
"We are pointing out that the direction of travel for both hospitals and intensive care is going in the wrong direction, particularly in these areas that have seen rapid increases in cases," he said.
There had been a "significant uptick" in the number of people being admitted to intensive care, especially in the North East and North West of England but also in London.
Although the level of cases remained far below the NHS intensive care capacity, it was "definitely heading the wrong way".
The latest figures showed a further 7,108 lab-confirmed cases of coronavirus in the UK, slightly down on the 7,143 reported on Tuesday.
The Government also said a further 71 people had died within 28 days of testing positive for Covid-19 as of Wednesday. This brings the UK total to 42,143.
Separate figures published by the UK's statistics agencies show there have now been nearly 57,900 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
The Government said there were 312 Covid-19 patients in mechanical ventilator beds as of Tuesday, and 2,252 Covid-19 patients currently in hospital, as reported on Monday.
Prof Whitty said the "small number of deaths now" compared with the height of the outbreak "shouldn't reassure us that we won't be, in relatively short order, in quite difficult places – certainly in the regions where we are seeing significant growth at the moment, where pressure on the NHS could happen sooner rather than later if we can't get on top of it really quite fast".
The Government's chief scientific adviser Sir Patrick Vallance said: "It is very clear that rates are still going up.
"And, so, we don't have this under control at the moment."
In other developments:
– Local lockdowns will be introduced in Denbighshire, Flintshire, Conwy and Wrexham in North Wales from 6pm on Thursday, meaning that a third of the UK population will be subject to some form of extra restriction.
– Planned surgery is being suspended as a result of restrictions imposed at the Royal Glamorgan Hospital in Llantrisant, South Wales, after 82 coronavirus cases were identified.
– Police chiefs said crime was returning to pre-pandemic levels and called for extra funding for officers to enforce new coronavirus rules.
– Merseyside's leaders expect extra local restrictions to be imposed but warned that the Government must prevent a "hammer blow" to the region's economy.
– Commons Speaker Sir Lindsay Hoyle rebuked Mr Johnson's Government for treating Parliament with contempt over the way coronavirus regulations had been introduced.
– MPs voted to extend the temporary powers in the Coronavirus Act after ministers promised to give Parliament a greater say over national measures in future.
Mr Johnson has said the way the virus is spreading may be different now to the first wave in March.
"We are seeing some very clear local peaks," he said.
"It may be that this is a more localised phenomenon this time in which case all the more reason for us to concentrate on these local solutions as well as these national solutions."
Prof Whitty said it was possible cases could be "highly concentrated in certain areas", as happened in Spain and Italy.
"But it is far too early to say that," he added.
"We have got a long winter ahead of us and a lot could happen over that time.
"So I think to predict forward from here would be a big mistake. But it is certainly possible that if we all work together, if we all follow the guidance, then we could actually contain it within the areas where it is in the way that happened, to some degree, in Italy and Spain."
Labour leader Sir Keir Starmer said: "There's got to be – if you like – a national effort to prevent a second lockdown.
"But the Government's side of the bargain here is to have a very clear strategy for keeping that infection rate down and we don't see that strategy."