Two of the patients had recently travelled back from Italy while the other had returned from Asia, Chief Medical Officer Professor Chris Whitty said.
The three cases - one in Gloucestershire, one in Hertfordshire and another in Berkshire - are being investigated and any individuals who had contact with the patients are now being traced.
As of 9am today, more than 10,000 people in the UK had been tested for the virus, also known as Covid-19 - with 23 confirmed as positive.
It was not clear if the patient had contracted the virus "directly or indirectly" from somebody who had recently travelled abroad, Prof Whitty said on Friday.
He added that the patient had been transferred to a specialist NHS infection centre at Guy's and St Thomas'.
Former health secretary Jeremy Hunt, MP for South West Surrey, said on Twitter he was thinking of "clinicians, staff and patients" at the surgery during this "worrying time".
He added: "Thoughts today with new Covid19 patient and local GP with symptoms alongside their families."
This morning, health minister Edward Argar refused to comment on reports that a GP may have been infected with the virus.
"I'm aware of The Guardian report, but I'm going on the basis of what I've been told," he told BBC Radio 4's Today programme.
"I haven't had any details of that and I think it would be wrong to comment on speculation in the press without that detailed advice from the chief medical officer."
Mr Argar also defended the Prime Minister against criticism that he had been slow to act on coronavirus, having delayed chairing his first emergency Cobra meeting on the outbreak until Monday.
It comes as the Government prepares to bring in new emergency powers to help stop the virus spreading.
The PA news agency understands that this will give schools, councils and other parts of the public sector powers to suspend laws - including health and safety measures - to cope with a pandemic.
Elsewhere, a major real estate exhibition due to take place in Cannes next month announced the event would be postponed due to fears of the virus spreading.
MIPIM, which bills itself as the world's leading property market, was due to open on March 10 but has been rescheduled for between June 2 and 5.
First UK citizen to die
Meanwhile, a British man, reported to be in his 70s and said to have lived abroad, was confirmed as the first UK citizen to die from the virus on Friday.
The man, who was on board the Diamond Princess cruise ship quarantined off Japan's coast amid the outbreak, was the sixth person from the vessel to have died.
David Abel and his wife Sally were both on board the ship, where more than 700 tourists became infected, and are now undergoing treatment for the virus in hospital.
Mr Abel said in a YouTube video: "Sad news this morning, wasn't it? We awakened to that, to hear that one of the Brits has sadly passed away in hospital out here in Japan.
"Our thoughts, our concern is for all of the families left behind. We are fortunate, we're doing OK, we're being really, really well cared for."
The three new cases on Saturday takes the total number in England up to 21, while there has been one confirmed case in Northern Ireland and one in Wales.
Wales's chief medical officer Dr Frank Atherton said the first diagnosed patient in Wales had recently travelled back from Italy, the worst-affected country in Europe.
In Tenerife, hundreds of guests have been confined to the H10 Costa Adeje Palace after at least four tourists, including an Italian doctor, were diagnosed with coronavirus.
However, six Britons were among those who were told they could leave on Friday by Spanish authorities because they arrived at the hotel on Monday - after those who tested positive had been taken to hospital.
The number of people sickened by the virus climbed to more than 85,000 globally on Saturday and there were more than 2,850 deaths, most of them in China.