Health Minister Nadine Dorries has become the first MP to test positive for coronavirus, but Boris Johnson and members of the Cabinet will not be tested, despite concerns about the spread of Covid-19.
The Department of Health and Social Care (DHSC) said ministers would not need to undergo testing as Public Health England (PHE) worked to advise those who have been in close contact with Ms Dorries.
PHE said it had assessed the risk of Ms Dorries’ individual close contacts and only those with symptoms need to self-isolate.
Despite Ms Dorries having recently been inside Parliament, Baroness Nicky Morgan told ITV News that it should "absolutely" continue.
She said: "The scrutiny of Parliament at this important time is absolutely critical and I think it would send completely the wrong signal for Parliament not to be sitting."
One of those instructed to self-isolate after contact with Ms Dorries is Labour MP Rachael Maskell, who said she was quarantining herself on the advice of 111 following a meeting with the health minister last Thursday.
For each Covid-19 case, a risk assessment is carried out and advice tailored to that group, a spokeswoman said.
Ms Maskell told ITV News she was feeling "absolutely fine" and insisted Parliament should "not shut down" over the virus.
Despite concerns that the virus is now present in Parliament, with Ms Dorries office being cordoned by police, Ms Maskell says there are technical "solutions out there to ensure that our parliament can continue to function".
She urged Prime Minister Boris Johnson to seek advice from the NHS after reports he shared a room with Ms Dorries at an International Women's Day event.
"There's nothing special about the prime minister, he's another human being who should be acting according to the advice of public advice England," she said.
"I advise him, as I would anybody, is to contact NHS 111 and make sure he is fulfilling those hygiene responsibilities."
Ms Dorries met up to 12 of her constituents in a surgery at her Mid Bedfordshire constituency on Friday and all those in attendance are advised to seek medical advice.
Steven Dixon, chair of the Mid Bedfordshire Conservative Association said the surgery took place at The Flitwick Club, a private members club, which is now undergoing a deep clean as a precaution.
In a statement, Ms Dorries said: "I can confirm I have tested positive for Coronavirus.
"As soon as I was informed I took all the advised precautions and have been self-isolating at home."
"Public Health England has started detailed contact tracing and the department and my parliamentary office are closely following their advice."
On Twitter, Ms Dorries said she hopes she is over the worst of it and was more concerned for her 84-year-old mother who is currently living with her.
She said: "It’s been pretty rubbish but I hope I’m over the worst of it now.
"More worried about my 84yo mum who is staying with me and began with the cough today.
"She is being tested tomorrow. Keep safe and keep washing those hands, everyone."
Health Secretary Matt Hancock tweeted saying Ms Dorries "has done the right thing by self-isolating."
Mr Hancock continued: "Really sorry to hear Nadine has tested positive for coronavirus.
"She has done the right thing by self isolating at home, and both NHS and PHE staff have been brilliant. We all wish her well as she recovers."
He added: "I understand why people are worried about this disease. We will do all we can to keep people safe, based on the best possible science."
ITV News Political Correspondent Paul Brand tweeted saying Ms Dorries has been in "close proximity to hundreds of MPs.
He said: "Nadine Dorries voted in the Commons twice last Wednesday, meaning she will have been in close proximity to hundreds of other MPs, if only briefly.
"Will be a huge job to trace all those she’s been in contact with, as she now self-isolates and recovers at home."
The UK may experience its peak number of coronavirus cases within the next fortnight, England's deputy chief medical officer has admitted.
Dr Jenny Harries defended the Government's decision to delay closing schools and the introduction of other tactics, adding experts are assessing new cases on an hourly basis to ensure a "balanced response".
Garry Graham, deputy general secretary of the Prospect trade union which represents staff in Parliament, called for the option of closing the Palace of Westminster to visitors to be considered in response to the coronavirus crisis.
He said: "As the union for House staff we are seeking urgent clarification from the Leader of the House what action he is taking to protect workers following news that a minister and a member of her team have contracted coronavirus.
"While we understand the reluctance to shut the House at this stage, we think measures short of a full closure may be appropriate at this time. "In particular, we ask that the option of closing the Houses of Parliament to visitors be considered.
"Dedicated House staff will do all they can to ensure the machinery of democracy continues to function but they need to hear that reasonable steps are being taken to protect their well-being."