Public Health England have warned that widespread transmission of the coronavirus across the UK is 'highly likely'.
It comes as the Prime Minister gathers ministers for an emergency Cobra meeting.
Professor Paul Cosford, emeritus medical director of Public Health England (PHE), said more cases could be challenging for the country and urged people to take simple steps such as washing their hands to reduce the risk of infection.
When asked on BBC Breakfast if widespread infection was inevitable, he said: "I wouldn't say it's inevitable but it is now highly likely."
Later on ITV's Good Morning Britain, Prof Cosford added that "the extent of infection we are seeing in other countries suggests it is likely that we will see more widespread infection in the UK".
He said: "We should expect at times that might be quite challenging for us, it is therefore very important that we do everything we can to reduce the spread of infection.
"At the moment, the vast majority of cases we see in the UK are still linked to countries where there is more widespread infection, either in Italy or South East Asia.
"It is true to say there is a small number now where it is much more difficult to find that link, and that is leading us to think we may well see more widespread infection in the UK fairly soon.
"It could happen in the next few days or it could take a little longer."
Prof Cosford was also interviewed for Radio 4's Today programme, where he said evidence showed widespread infection was looking "much more likely".
He said most people would only suffer mild infection, and that children and healthy adults seem to be at much lower risk of serious complications.
"It's older people and people with severe underlying conditions that we will be particularly concerned about," he said.
The professor has also warned that there could come a point "where we reduce social contact if we see more widespread transmission".
This could involve asking "people to isolate themselves at home if there's a member of their family who's infected".
He added: "We may well get to a position where we say carry on going to school, carry on going to work but if you can work from home that's a very sensible thing to do, and think of all the different ways you can reduce your social contact outside of those activities."
His comments come as Boris Johnson gathers ministers for a Cobra meeting to draw up a battle plan for dealing with coronavirus.
Mr Johnson was criticised by Labour for being a "part-time" Prime Minister as the UK coronavirus toll climbed to 36 cases over the weekend.
The Cobra meeting will be attended by senior ministers as well as England's chief medical officer Professor Chris Whitty and chief scientific adviser Sir Patrick Vallance.
Scotland's First Minister Nicola Sturgeon is also expected to take part after a Tayside resident - who had recently travelled from Italy - was diagnosed with the virus.
Shadow health secretary Jonathan Ashworth said Labour would support putting cities in lockdown if the medical advice showed it was necessary.
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