Video report by ITV News Correspondent Lucy Watson
The number of confirmed coronavirus cases in the UK has leapt to 36 after Scotland confirmed its first case.
The Scottish Government said a Tayside resident who recently returned from Italy had tested positive for the virus.
It comes after 12 new patients were identified in England on Sunday.
Three of the latest cases in England are family members of a man from Surrey who tested positive on Friday, becoming the first person to contract the virus within the UK.
Another new patient, from Essex, has no relevant travel to an affected area, Professor Chris Whitty, Chief Medical Officer said on Sunday.
Prof Whitty added investigations were ongoing as to whether the patient had contracted it "directly or indirectly" from an individual who had recently travelled abroad.
Of the eight remaining cases, six had recently travelled from Italy, while two had been in Iran.
Two Leeds residents both became infected while in Iran
Two Gloucestershire residents became infected while in northern Italy
A Bradford resident caught Covid-19 in Italy
A Bury resident became ill while in Italy
The remaining patients are from London, Hertfordshire and Gloucestershire
All of the newly identified cases are being investigated and health officials have begun tracing anyone who had close contact with them.
As of 9am on Sunday, more than 11,000 people have been tested for coronavirus in the UK - with 35 confirmed as positive.
On Saturday, three more cases of Covid-19 were diagnosed, with one each in England, Wales and Northern Ireland.
The new cases come after the Health Secretary conceded it was "inevitable" that the deadly virus would continue to spread across the UK and the Government outlined a new “battle plan” and said it will not "take anything off the table" in its response to the spread of Covid-19.
Meanwhile, Prime Minister Boris Johnson visited Public Health England to discuss attempts to limit the spread of the virus.
Also on Sunday, the Department of Health and Social Care announced that every department will have a ministerial lead on the virus while a cross-Whitehall “war room” is being set up to roll out an enhanced public information campaign.
Health Secretary Matt Hancock said he is still hopeful of containing Covid-19 as he detailed the new approach to pandemic preparation on Sunday, but added he has not ruled out shutting down cities if the coronavirus outbreak escalates.
Speaking to ITV News, Mr Hancock said the Government has a "full battle plan for the coronavirus outbreak".
He said the first step is to "contain" Covid-19 to try and "stop this from becoming a pandemic right across the world and endemic across this country".
Mr Hancock said the long-term strategy for ensuring Covid-19 was contained was attempting to delay its “peak” until the summer, as the virus will not spread so easily in warmer weather.
If the outbreak worsens, the next phase of the Government’s plans could include encouraging people to work from home and recalling retired doctors and nurses.
Mr Hancock added the NHS was ready to deal with further cases of coronavirus, with more than 5,000 emergency critical care beds available.
The Health Secretary confirmed that "population distancing measures", such as banning public gatherings and cancelling football matches, could be considered by the Government, while closing schools may be "necessary".
Two of the cases confirmed on Saturday were staff members at primary schools.
On Sunday, St Mary's School in Tetbury confirmed a member of staff was one of those who tested positive for Covid-19 on Saturday.
In a letter to parents, headteacher Jo Woolley said that while it was not necessary to close the school from a health perspective, it will close until at least Wednesday due to "operational difficulties" with staff members.
ITV News Wales & West of England Correspondent Rupert Evelyn reports on the latest at St Mary's School
She said: "Whilst I fully understand this will cause anxiety amongst the school community, I can assure you all necessary steps are being taken to minimise risk to others.
"A deep clean of the school was carried out on Saturday, February 29.
"All people who have had contact with the person have already been identified, contacted and know if they need to exclude themselves from school."
Meanwhile on Saturday, the headteacher of Willow Bank Infant School in Berkshire urged parents to “remain calm and follow the recommended hygiene procedures” after a staff member there also tested positive for Covid-19.
“The school will be shut for some days to allow for a deep clean and to ensure that the risk of infection remain(s) low,” Michelle Masters said.
Health officials are also tracing anyone who had close contact with the third case confirmed on Saturday - a resident in in Hertfordshire.
All three of the cases confirmed on Saturday had either been to Italy or Asia, Prof Whitty said.
It came as Donald Trump banned travel to Iran after the US reported its first death from the virus.
The president added that he was considering additional restrictions, including closing the border with Mexico in response to the outbreak.
Elsewhere, the husband of British-Iranian woman Nazanin Zaghari-Ratcliffe believes she has contracted coronavirus at the prison where she is being held.
Richard Ratcliffe said his wife has repeatedly asked to be tested for the virus at the Evin prison in Tehran after suffering from a “strange cold”.
Although there are currently no confirmed cases at the prison, Covid-19 has spread rapidly across Iran – with at least 54 dead amid 978 patients identified.
On Sunday the Foreign Office confirmed it was pulling all non-essential staff out of its embassy in Tehran due to increasing concerns about the spread of the virus.
The Foreign and Commonwealth Office (FCO) has called on the Iranian government to “immediately allow” health professionals into the prison to assess British-Iranian dual nationals.
Holiday operator Tui said on Saturday evening it would be making arrangements for Britons at a coronavirus-stricken hotel in Tenerife who test negative to return to the UK.
Around 160 Britons were among hundreds of guests put into quarantine at the four-star H10 Costa Adeje Palace after at least four holidaymakers were diagnosed with Covid-19.
ITV News Correspondent Geraint Vincent reports from Tenerife:
Spanish authorities have since said the risk of infection for any Britons staying at the hotel was low, although Public Health England (PHE) advised anyone travelling back to self-isolate until March 10.
It comes amid reports that a fifth man at the hotel has tested positive for coronavirus.
The number of people sickened by the virus has climbed to more than 86,000 globally and there have been more than 2,900 deaths, most of them in China.