Health Secretary Matt Hancock refused to guarantee that pubs in England would be allowed to open this weekend as ministers considered options to limit the spread of the virus.
Prime Minister Boris Johnson is expected to address the nation on Tuesday to outline any new restrictions that may be introduced.
Whitty said: "If this carried on unabated... the number of deaths directly from COVID. will continue to rise, potentially on an exponential curve, that means doubling and doubling and doubling again".
Pubs, bars and other hospitality places in the United Kingdom will have to close at 10pm from Thursday, as the British federal government enforces new restrictions to attempt to suppress a surge in coronavirus cases, Euronews reports.
The advisors' comments have fueled speculation that the government is preparing the ground for a second national lockdown, or other hard measures, in order to get cases back to a sustainable level.
Cases are increasing, hospitalisations are following, he said. It was eased starting in June as cases began to fall, but that trend has now been reversed.
Today, Johnson spoke with the leaders of devolved administrations in Scotland, Wales, and Northern Ireland.
The UK could be facing 50,000 new Covid-19 cases a day by mid-October, leading to 200 deaths a day a month later if the current rate of infection is not halted, the Government's chief scientific adviser Sir Patrick Vallance has warned.
Whitty stressed that infection rates are rising among all age groups and said it is not acceptable for individuals to ignore health guidelines and engage in risky activity.
"So, this is not someone else's problem, this is all of our problem". "This is all of our problem". It also said those breaking quarantines could face fines up to 10,000 pounds ($12,800).
Britain has the highest confirmed virus death toll in Europe, at 41,877 deaths, according to a tally by Johns Hopkins University. Experts say all such figures understate the true impact of the pandemic.
Parts of the Spanish capital Madrid went into a tough new lockdown on Monday.
A spokesperson from the Department of Health said: "The latest findings for the period 22 August and 7 September - testing more than 150,000 volunteers - indicate cases were doubling every seven to eight days".
That could lead to 200 new deaths per day a month later, he warned.
Britain recorded another 4,368 infections overnight on Monday, bringing total number of coronavirus cases to 398,625.
"We know this won't be easy, but we must take further action to control the resurgence in cases of the virus and protect the NHS".
Mr Hancock said he wanted Christmas to be "as normal as possible" and suggested a vaccine could be available early next year "if all goes well".
Shares in Britain's listed pubs and restaurant groups fell sharply on Monday in anticipation of the move.
"Clearly, we're taking a gander at the spread of the pandemic as it advances in the course of the most recent couple of days, and there's no doubt, as I've said for half a month at this point, that we could expect, and we are presently observing, a subsequent wave coming in", he said.
The rise in infection rates comes as lawmakers across the political spectrum criticize the government's testing program.
It's not yet clear when the new rules will come in, or how long they will last for.