It comes as United Kingdom ministers make final decisions on what national measures are needed to tackle rising cases, with Health Secretary Matt Hancock strongly hinting that separate households could be prevented from mixing.
Chief Medical Officer Professor Chris Whitty, who had been speaking alongside Sir Patrick, said the government were trying to asses the best way to "manage the spread of the virus ahead of a very challenging winter period".
Sir Patrick said ONS data shows cases are doubling "roughly" every week.
"50,000 cases per day would be expected to lead a month later, so the middle of November, to 200-plus deaths per day".
"The challenge therefore is to make sure the doubling time does not stay at seven days".
In order to curb the rise in coronavirus cases in the United Kingdom, it is now illegal for groups of more than six to meet up. The answer is no.
"We need to reduce our individual risk, washing hands and wearing masks in places that are contained and maintaining space between people especially when in doors".
"We need to reduce unnecessary contacts between households".
"We all know we can not do this without some significant downsides".
"If we don't do enough the virus will take off and at the moment that is the path that we are clearly on and if we do not change course then we're going to find ourselves in a very hard problem".
Sir Patrick said: "What we see is that something under 8% of the population have been infected as we measure the antibodies".
"It's not indefinite and ... science will in due course ride to our rescue".
Cases in Britain are on the increase in what Prime Minister Boris Johnson has labelled a second wave of the virus, with large areas of the country subject to restrictions on social freedom and London expected to be next in line.
"If we do have to take action, it will be different to last time and we've learnt a huge amount about how to tackle the virus", he told ITV.
"But I'm afraid, although that would be great if that were true, we see no evidence that is the case".
"Schools aren't where a lot of the transmission happens, it's more about people socialising", he said.
When asked why the Prime Minister was not going to be part of Prof Whitty's public address, Mr Shapps said: "What he wants to do, quite rightly, is allow without politicians there, to allow scientists to set out the picture to the country".
"If this runs out of control now, we'll have to take heavier measures in the future", Hancock said.
"There's a series of different vaccines, but we are talking about - essentially, for it to have an impact on how we live our lives - we're talking about the start of next year".
He added: "Hopefully in the first few months - there's still a chance of it coming on stream before Christmas, but we've then got to roll it out and the first people who will get it are the people who are most vulnerable - people in care homes, older people".
Ministers were reported to be split on how far any new restrictions should go.
However, as of Tuesday, about 13.5 million people across the United Kingdom will be facing some form of local restrictions, including 10pm curfews for pubs and restaurants, as the authorities grapple with the disease.