In a Commons statement, he said: "The situation facing the country is increasingly serious.
"Globally and at home the number of cases continues to rise.
"As of 9am today there were 51 confirmed cases in the UK and it's becoming more likely that we will see widespread transmission here in this country."
Mr Hancock told the Commons the Government was working on “preventing the disease from taking hold in this country for as long as reasonably possible”.
He said: "This approach also buys time for the NHS to ramp up its preparations.
"If the number of global cases continues to rise, especially in Europe, the scientific advice is that we may not be able to contain this virus indefinitely."
Bradford South MP, Labour’s Judith Cummins, asked the Secretary of State how care homes would be supported during the outbreak.
He told her the elderly were some of the most at risk and the Government would have specific plans for care homes.
Yvette Cooper, Labour MP for Normanton, Pontefract and Castleford, raised concerns in the about the carers of elderly relatives and what support there would be "both for them where they may not be getting any sick pay, but also for the elderly relatives who depend on some urgent support".
Mr Hancock said: "We are very concerned about this issue and in the communications... that we'll publish soon to social care providers we will address precisely the issue that she raises... volunteers are not the only part of the answer to this problem."
He also said that social media companies are playing a "very responsible role" in addressing the coronavirus outbreak.
Conservative James Wild, MP for North West Norfolk, asked: "People are understandably concerned, and I've been contacted by some of my constituents about potential treatments that are appearing on the internet including vitamin therapy.
"Can (Mr Hancock) send a clear message from this Chamber that it's the NHS and the Government that will provide the authoritative advice on medical treatments and will he work with social media companies to remove any misleading content?"
Mr Hancock responded: "Fake news in response to a virus like this can be dangerous and damaging to health and it should be taken down.
"I'm working with the social media companies, I spoke to the main social media companies yesterday. The biggest social media companies are playing a very responsible role - if you search on Google, then the top two sites that come up for coronavirus are World Health Organisation, the NHS is third - and they are promoting good, high quality, medically informed advice.
He added: "The other social media platforms, the major ones, that we're working with are also taking this very seriously."
The Health Secretary said the Government has increased the number of 111 call handlers by 500 and that as of 11am today "10 schools are closed".
He added that a wider communications campaign will be launched on Wednesday and that the Government are "currently engaged with just over a dozen companies to try to come up with a bedside test".
Questioned on dwindling supplies of hand sanitising gel and whether the UK will have enough supplies of paracetamol, Mr Hancock replied: "Our no-deal planning and our no-deal stockpiles are playing an important part in making sure we are fully prepared and ready."
Pushed on his earlier remark that "reacting too early carries its own risk" by Leeds Central Labour MP Hilary Benn, Mr Hancock said: "I'd highlight two. The first is that there is an economic and social impact of disruption - if an action has no medical benefit then there is no need for that disruption.
"But the second is a medical risk which is that behavioural science and experience from previous similar such outbreaks shows that if you ask people to do things too early which are disruptive to their normal life then they may try to return to normal earlier than they otherwise would."