The Department of Health and Social Care (DHSC) said on Sunday that 3,109 tests have been carried out in the UK so far, with nine positive results.
This is an increase of 117 tests on the 2,992 reported on Saturday.
The number of positive tests remains at nine, with eight of those patients now discharged from hospital after recording two negative tests for the strain known as Covid-19.
But "millions" of Britons with flu-like symptoms could be told by authorities to "self-isolate" by staying at home for a fortnight if the UK's number of confirmed cases passes 100, the Sunday Telegraph has reported.
The paper said that senior NHS managers have been told that the service will stop testing for Covid-19 "once around 100 cases have been confirmed" across Britain.
In the last week hospitals have created "isolation pods" to keep those being tested away from other patients, it added.
If the number of cases rises significantly those with coughs and colds may be asked to stay home to limit the chance of the outbreak spreading.
The DHSC did not comment when asked about the self-isolation direction.
NHS England said on Saturday that all 94 people in quarantine at Arrowe Park Hospital on the Wirral had been released.
They had been kept in isolation at the hospital after returning to the UK from Wuhan in China - the centre of the outbreak.
More than 100 people remain in isolation at the Kents Hill Park Hotel in Milton Keynes after being on a later rescue flight, the NHS added.
Health Secretary Matt Hancock said: "I am also pleased that eight of the nine individuals who tested positive for coronavirus have now been successfully treated and discharged from hospital.
"I want to stress that any individuals who are discharged from hospital are now well and do not pose any public health risk to the public."
"Again, this is evidence of how well prepared our NHS is to deal with the Wuhan coronavirus."
Britons on board the quarantined Diamond Princess cruise ship in Japan have said they fear being stuck in isolation beyond the initial February 19 deadline.
So far 355 of the 3,500 people on board the ship moored at Yokohama Port near Tokyo have tested positive for the virus.
Princess Cruises president Jan Swartz said that Japanese officials may extend the quarantine for guests who have shared cabins with someone who has tested positive for the virus.
She added: "We also now understand the Japanese may handle a select group of guests differently, anyone who had close contact with a person who tested positive - such as a cabin mate - may have to restart their quarantine from the date their close contact ended."
But Briton David Abel said on Sunday that passengers had heard they could be stuck on board for up to two months.
In a video on YouTube Mr Abel added: "To cut a long story short we could be here another month, not two weeks extra.
"We could be here for six, seven, eight weeks, that's what we've heard."
The first death from the virus outside Asia was confirmed in France on Saturday.
French Health Minister Agnes Buzyn said an elderly Chinese tourist had become the first death to the virus in Europe, Reuters reported.
The patient, a Chinese tourist from the province of Hubei that includes Wuhan, had arrived in France on January 16 and suffered a lung infection caused by the virus.
The death toll in mainland China has risen by 142 to 1,665.
Chinese authorities also reported the number of new cases has fallen for the third straight day to 2,009.
The number of people infected globally stands at 68,500, according to the country's National Health Commission.