A patient in Essex has become the second person in the UK to test positive for coronavirus without having recently travelled abroad, fuelling concerns that the virus is circulating in Britain undetected.

Prof Chris Whitty, the chief medical officer for England, said the patient “had no relevant travel” and an investigation was under way to determine whether the patient contracted the virus directly or indirectly from someone who had recently returned from overseas.

The case suggests the country is edging closer to the point where containment becomes impossible because the virus is being spread by people who are either unaware they are infected, or are diagnosed too late to prevent onward transmission.

The Essex patient was among 13 new cases reported on Sunday, bringing the total UK infections to 36. It is the largest single-day increase of new cases in the UK so far. One of the new cases is the first to be reported in Scotland, while two cases in total had previously been reported in Northern Ireland and Wales.

The patient in Scotland, who is a resident of the Tayside area and had recently travelled from Italy, has been admitted to hospital and is receiving treatment in isolation.

Nicola Sturgeon, Scotland’s first minister, chaired a meeting of the Scottish government resilience committee on Sunday evening and will be taking part in a similar meeting chaired by Boris Johnson on Monday morning.

Peter Openshaw, a professor of experimental medicine at Imperial College London, said: “This really adds to the supposition that many are now making that this one is going to be very hard to put back in the box. It makes it particularly difficult to control any outbreak if there are people who don’t know they’re spreading it.”

Johnson will chair a Cobra meeting on Monday to review the next steps aimed at containing the virus, and he will tell those signing off the strategy that the government will “stop at nothing” to fight the disease.

The meeting will be attended by senior ministers as well as Whitty and chief scientific adviser Sir Patrick Vallance in order to ratify the government’s proposed countermeasures.

The prime minister is set to tell those at the meeting: “The number of coronavirus cases around the world is rising every day – and the UK is no exception. There now seems little doubt that it will present a significant challenge for our country.

“But we are well prepared, and the government and the NHS will stop at nothing to fight this virus. This battle plan lays out in detail the measures we could use – if and when they are needed.”

Johnson had been dubbed a “part-time” prime minister by critics for failing to take charge of a Cobra meeting before this week.

The health secretary, Matt Hancock, confirmed on Sunday that the government would publish its approach to coronavirus this week but conceded it was inevitable that the virus would continue to spread across the UK. The NHS is planning to bring doctors out of retirement to cope if the outbreak escalates and Hancock did not rule out following China’s lead and isolating cities to contain the virus.

“There is clearly a huge economic and social downside to that,” Hancock told the BBC’s Andrew Marr Show. “But we don’t take anything off the table at this stage because you have to make sure you have all the tools available if that is what is necessary.”

Facebook Twitter Pinterest Boris Johnson: ‘I don’t want to go now into the kinds of things that might be necessary.’ Photograph: Henry Nicholls/PA

Emergency powers to slow the spread of the virus, if it becomes endemic, would only be temporary, Hancock added. He said “population distancing measures” such as banning public gatherings and cancelling football matches might be considered and closing schools could become necessary.

On Friday, a man from Haslemere in Surrey became the first person known to have caught the infection in the UK. Three of the men’s relatives, one also from Surrey and two from West Sussex, are among the new cases, forming an “adult family cluster”, said James Mapstone at Public Health England. At the weekend, the Prince of Wales pub in the town closed for deep cleaning after landlords said one of its customers had tested positive.

Paul Hunter, a professor of medicine at the University of East Anglia, said: “Although it may still be possible to prevent a community-wide epidemic, this is looking increasingly unlikely and we should be prepared to cope with a more widespread epidemic on our shores.”

Q&A How can I protect myself and others from the coronavirus outbreak? Show Hide The World Health Organization is recommending that people take simple precautions to reduce exposure to and transmission of the coronavirus, for which there is no specific cure or vaccine. The UN agency advises people to: Frequently wash their hands with an alcohol-based hand rub or warm water and soap

Cover their mouth and nose with a flexed elbow or tissue when sneezing or coughing

Avoid close contact with anyone who has a fever or cough

Seek early medical help if they have a fever, cough and difficulty breathing, and share their travel history with healthcare providers

Advice about face masks varies. Wearing them while out and about may offer some protection against both spreading and catching the virus via coughs and sneezes, but it is not a cast-iron guarantee of protection Many countries are now enforcing or recommending curfews or lockdowns. Check with your local authorities for up-to-date information about the situation in your area. In the UK, NHS advice is that anyone with symptoms should stay at home for at least 7 days. If you live with other people, they should stay at home for at least 14 days, to avoid spreading the infection outside the home.

Of the remaining eight new cases, six had recently returned from Italy and two from Iran. All of the new patients, from London, West Yorkshire, Greater Manchester, Hertfordshire and Gloucestershire, are being investigated and their close contacts traced.

The sudden rise in cases came as health authorities scrambled to track down people who had come into contact with a 35-year man from Shenzhen in China, who had been working in Bristol and tested positive for coronavirus after taking a Cathay Pacific flight from Heathrow to Hong Kong on Thursday.

A statement from the Guangdong health commission late on Sunday said authorities in Shenzhen had declared an “imported case” of the coronavirus after the man tested positive. It is unclear whether or not he became infected in the UK, but Chinese authorities said two of the patient’s colleagues in the UK had reported coughs and fever.

The man travelled from London to Hong Kong on 27 February on Cathay Pacific flight CX250. After landing in Hong Kong he took a ferry to Shekou port and from there entered mainland China.

While the man’s temperature was normal on arrival, he developed a cough and fever on 29 February and was driven to a hospital where he tested positive for coronavirus. He is now having treatment in Shenzhen, where his condition was described as stable.

Chuang Shuk-kwan, the director of the infectious disease division of the Centre for Health Protection in Hong Kong, advised all passengers on Thursday’s Cathay CX250 flight from Heathrow to Hong Kong, or on ferry number 3A109, to call the centre’s hotline and to be “aware of the health situation”, and seek medical help or quarantine if necessary. A spokesperson for Cathay Pacific said the plane was being disinfected and the airline was helping authorities trace passengers who came into close contact with the man.

Among measures announced by the Department of Health and Social Care on Sunday were a ministerial lead on the virus in every department and a cross-Whitehall “war room” to coordinate a beefed-up public information campaign.

One of the newly confirmed cases is a patient from Bury in Greater Manchester, who is being treated at a specialist NHS infection centre, according to Bury council. Will Welfare, the interim deputy director of health protection for Public Health England North West, said the agency was tracing people who had close contact with the patient, who became infected while in Italy.

Another case, identified on Saturday, is a member of staff at St Mary’s school in Tetbury, Gloucestershire. The school has been closed until at least Wednesday because of “operational difficulties” with staff rather than any ongoing health risk, according to a letter sent to parents from Jo Woolley, the headteacher. She said a deep clean was carried out on Saturday and that all people who had contact with the infected staff member had been spoken to.

“The thing I would urge every organisation and every business to do is to really start planning, as of now, for how people are going to manage to work remotely and cover each other’s jobs in the event that people have to take time off from work,” said Openshaw. “It’s planning for resilience in the eventuality that the spread is going to continue.”