Health minister and Conservative MP Nadine Dorries has been diagnosed with coronavirus.
Ms Dorries said she has been self-isolating at home. Labour MP Rachael Maskell said she has since been told to do the same as she had met Ms Dorries.
The Department of Health said Ms Dorries first showed symptoms on Thursday - the same day she attended an event hosted by the prime minister.
Six people with the virus have died in the UK, which has a total of 382 cases.
The latest person to die was a man in his early 80s who had underlying health conditions.
Meanwhile, a 53-year-old British woman has become the first person with Covid-19, the disease caused by the virus, to die in Indonesia, according to local media reports.
It is not clear whether the woman - who was reportedly critically ill with multiple health conditions - died due to the virus.
The Foreign and Commonwealth Office said it is "supporting the family of a British woman who has died in Indonesia and are in contact with local authorities".
The government is unveiling its first Budget, amid growing fears about the impact the outbreak will have on the UK economy.
Chancellor Rishi Sunak has pledged the NHS will get "whatever resources it needs" during the crisis as well as a "temporary coronavirus business interruption loan scheme" to support small and medium-sized businesses.
He also said the government will meet the cost of statutory sick pay for firms with up to 250 people, and people who are self-employed and fall sick will be eligible for benefits from day one.
The Bank of England earlier announced an emergency cut in interest rates from 0.75% to 0.25% in response to the economic impact of the coronavirus outbreak
It is not known how many meetings Ms Dorries had attended at Westminster or in her constituency in recent days, but she was at an event at Downing Street last Thursday to mark International Women's Day.
She also held a surgery in her constituency on Friday morning which was attended by up to 12 people, according to Steven Dixon, chair of the Mid Bedfordshire Conservative Association.
Mr Dixon said the details of all those who attended the surgery have been passed to the NHS.
The Flitwick Club, where the surgery took place, is undergoing a deep clean as a precaution.
The Department of Health said ministers - including the prime minister - would not need to undergo testing as Public Health England (PHE) has assessed the risk of Ms Dorries' close contacts and only those with symptoms needed to self-isolate.
But Labour MP Rachael Maskell tweeted she has been told by NHS 111 to self-isolate "as a result of a meeting" she had with Ms Dorries last Thursday.
Ms Dorries, who began her career as a nurse, later tweeted it had been "pretty rubbish but I hope I'm over the worst of it now".
But the 62-year-old added she was worried about her 84-year-old mother who was staying with her and began to cough on Tuesday.
In other developments:
- The chief executive of NHS England Sir Simon Stevens announced plans to invite "up to 18,000 third year undergraduate nurses to help out on the frontline"
- NHS England is scaling up its capacity for testing people for the infection. Public Health England, which has already carried out more than 25,000 coronavirus tests across the UK, is set to expand the number of people it can test a day to 10,000 - currently 1,500 are being carried out
- Confirmation of any positive test results will also be accelerated with most people getting a result back within 24 hours
- Health Secretary Matt Hancock is to give a statement to MPs at 19:00 GMT on Wednesday.
- Manchester City's Premier League match against Arsenal on Wednesday has been postponed as several Arsenal players are in self-isolation after coming into contact with Olympiakos owner Evangelos Marinakis, who tested positive for the virus
NHS chief scientific officer Prof Dame Sue Hill said the health service was preparing to cope with more cases.
"Every hospital across the country, and the healthcare professionals who run them, are now actively planning to respond flexibly to manage new demand."
Scotland, Wales and Northern Ireland will be expected to roll out their own testing services, but there will be some shared capacity between nations, depending on need.
There are 91 in London, with the next highest infected area being the south-east, with 51 cases. Cases by local council area in England can be viewed here.
The latest person to die, on Monday, was a man in his 80s, with underlying health conditions, who was being treated at Watford General Hospital.
He caught the virus in the UK and officials are trying to trace who he had been in contact with.
The Foreign Office has warned Britons against all but essential travel to Italy, which is experiencing the worst outbreak outside China.
Italy has introduced strict travel restrictions, with people being told to stay home, seek permission for essential travel, and give justification if they want to leave the country.
The Foreign Office is advising anyone arriving in the UK from Italy since Monday evening to self-isolate for 14 days.
The government says it has facilities to accommodate Italian visitors to the UK should they need to self-isolate.
British Airways has cancelled all of its flights to and from Italy until 4 April, and has asked staff to take voluntary unpaid leave.
Easyjet, Ryanair and Jet2 are also cancelling their flights on Italian routes, though EasyJet will operate "rescue flights" to bring British travellers home in the coming days.
'Enter shops one at a time'
"It's the weirdest holiday I think I've ever been on," said Hannah Butcher, from Newbury, Berkshire, who is in Rome with her husband for their first holiday alone since having a child.
"We arrived on Sunday. The advice then was as long as you're not going into Italy's red zone, you're OK.
"We're currently sitting in a restaurant and everyone here is in staggered rows because they have to sit one metre apart. It's quite weird seeing families spread across multiple tables."
She added that people are "only allowed to enter shops one at a time".
"All the attractions are closed; there are queues out the door of supermarkets and the butchers. There are police driving round making sure the rules are enforced and a noticeable armed police presence, presumably to keep order."
She said they were due to fly home with Ryanair on Wednesday morning and had not been informed of any flight updates.
In other developments:
- The government is considering a policy of "cocooning" groups of people who are most vulnerable, such as older people in care homes, who may be kept apart from the wider population
- Great Ormond Street children's hospital cancelled some non-essential cardiac operations for two weeks after a health worker in its cardiology department tested positive for the virus
- Royal Bank of Scotland, Lloyds and TSB banks said they would allow customers to defer mortgage payments if needed
- One of the UK's biggest insurers, Aviva, has cut back on the cover available in new travel insurance policies because of coronavirus, with people not able to add cover for "travel disruption"
- The Church of England has urged parishes to stop contact during services - including sharing the chalice and shaking hands for the sign of the peace.
- The Catholic Church of England and Wales has issued similar advice - advising parishes to remove holy water stoups; ban worshippers touching or kissing the Cross on Good Friday; and stop using shared hymn books and missals..
- British nationals who were on board the virus-hit Grand Princess cruise ship are being flown back to the UK where they will go into self-isolation
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