Boris Johnson said the UK should be "confident and calm" over the threat of coronavirus following a rise in the number of cases in the country.
The Prime Minister praised the response of the NHS and said anyone concerned should "simply follow their advice".
Meanwhile, it is understood two prisoners at HMP Bullingdon in Oxfordshire are being tested for the illness and are being held in isolation.
One of the men is understood to have been recently transferred from a Thai jail. They are both reported to be suffering flu-like symptoms.
As of Tuesday evening, a total of 1,358 people have been tested for coronavirus in the UK, of which 1,350 were confirmed negative and eight positive, the Department of Health said.
READ MORE: Scotland's coronavirus testing numbers double in 48 hours
Speaking in Birmingham, Johnson said: "We are a great country, we have got a fantastic NHS, we have got fantastic doctors and advice, and they should simply take the advice of the NHS.
"People have every reason to be confident and calm about all that kind of thing ... all the coronavirus, and any threats from disease."
It came as Steve Walsh, the businessman at the centre of a UK outbreak of coronavirus, thanked the NHS for his treatment and said he is "fully recovered".
Walsh, 53, from Hove in East Sussex, who is still in quarantine at St Thomas' Hospital in London, picked up coronavirus while at a conference in Singapore.
On his way back to the UK, he stopped off for several days at a French ski chalet, where five Britons were subsequently infected with the virus.
READ MORE: Coronavirus: Specialist test centres set up in Scottish hospitals
He is also linked to at least five further cases of coronavirus in the UK, including two doctors, one of whom worked at a Brighton surgery that has closed its doors.
Walsh is also linked to one male patient taken ill in Majorca.
Speaking from hospital, Walsh, a cub scout leader, said in a statement: "I would like to thank the NHS for their help and care - whilst I have fully recovered, my thoughts are with others who have contracted coronavirus.
"As soon as I knew I had been exposed to a confirmed case of coronavirus, I contacted my GP, NHS 111 and Public Health England.
"I was advised to attend an isolated room at hospital, despite showing no symptoms, and subsequently self-isolated at home as instructed.
"When the diagnosis was confirmed I was sent to an isolation unit in hospital, where I remain, and, as a precaution, my family was also asked to isolate themselves.
READ MORE: Virus cases rise as China faces anger over death of whistleblower
"I also thank friends, family and colleagues for their support during recent weeks and I ask the media to respect our privacy."
A spokeswoman for the Scout Association said Walsh had not been to any Scout meetings since his return to the UK, and wished him a quick recovery.
It comes as the World Health Organisation announced a name for the new coronavirus – Covid-19.
Also on Tuesday, Health Secretary Matt Hancock told MPs in the Commons that new funding was being launched immediately "to support any urgent works the NHS needs for the coronavirus response, such as the creation of further isolation areas and other necessary facilities."
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