People with symptoms as minor as coughs and colds could be asked to self-isolate within the next two weeks, the government warned on Monday, as Boris Johnson defended the government’s handling of the coronavirus crisis.

Speaking at a press conference with the prime minister, Chris Whitty, England’s chief medical officer, said that the step would be necessary in a new phase where “we will be having to ask members of the general public to do different things than they would normally do”.

Whitty said that would mean “a situation where we say everybody who has even minor respiratory tract infections or a fever should be self-isolating for seven days afterwards”.

The new measures were set out as Boris Johnson called for a “national effort” to tackle the virus, insisting that the experts “know how to defeat it”. He said the government was making extensive preparations to move to the “delay” phase of dealing with it – but meanwhile the best advice was still simply for people to wash their hands.

Downing Street’s approach to the outbreak has come under increasing scrutiny, as other countries including Italy and Ireland have taken more draconian measures, such as shutting schools and cancelling public events.

In other developments in the UK on Monday:

• The deaths of two more British people – both in their 70s with underlying conditions – were announced as the total number of infections grew to 319. A hospital worker at University Hospital Southampton tested positive for the virus, as did an office-based Transport for London worker.

• PHE said that the NHS would be brought in to ease the strain on its laboratories by helping to test samples from those displaying symptoms, doubling the number of tests that can be carried out each day from 2,000 to 4,000.

• The NHS set out plans to fight misinformation by working with social media companies to identify reliable sources and work to limit the spread of false claims.

• Labour leadership candidate Lisa Nandy said the threat of economic damage posed by the crisis was so severe that the Brexit transition period should be extended.

Experts have warned about the risk that if tough measures are taken too soon, “fatigue” may set in, prompting the public to disregard the advice just as the virus reaches its peak.

The government has been taking advice from behavioural experts and mathematicians, as well as doctors and scientists, in trying to judge the best approach.

Whitty said that from Tuesday the UK would also be screening more people in hospital with respiratory problems for coronavirus, rather than just those in intensive care.

The chancellor, Rishi Sunak, is expected to announce plans in Wednesday’s budget for ensuring that gig economy and low-wage workers are cushioned from the financial consequences of staying at home.

Measures are expected to include making universal credit available without the usual visit to the Jobcentre, and shortening the waiting time for Employment Support Allowance, the benefit that can offer temporary support for workers whose hours are reduced. Sunak will also set out more drastic economic stimulus measures that the Treasury could take later in the year if the worst-case scenario for the virus is realised.

At the Downing Street press conference on Monday, Johnson, Whitty and the government’s chief scientific adviser, Patrick Vallance, all rejected the idea that ministers were failing to do enough. “We are doing everything we can to combat this outbreak based on the very latest scientific advice,” the prime minister said. “We mustn’t do things with no or limited benefits.”

He said the government was “considering absolutely all measures,” and suggested timing was crucial.

Vallance said the measures being taken to contain and delay the outbreak were aimed at reducing the numbers who would be infected by 50%, and cutting the mortality rate among those who do catch it by 20%-30%.

In the House of Commons earlier on Monday, health secretary Matt Hancock faced a barrage of questions from MPs asking for better explanations of the government’s strategy.

Hancock’s Labour shadow, Jon Ashworth, asked for reassurance that GPs and hospitals would have the equipment they need.

Hancock struck a reassuring tone, saying the NHS was taking “necessary and proportionate” actions to tackle the outbreak. He said the NHS had record numbers of nurses and doctors, and the government was “scaling up intensive care beds” as well as increasing availability of ventilators, trained operators and oxygen.

The Tory MP Philip Hollobone said his constituents were struggling to understand why flights from quarantined areas of Italy were not being banned.

“The reason is that there are many UK citizens in that area who may want to come home, and also, crucially, the evidence shows banning flights from affected areas does very little to protect you,” Hancock said.

The government also came under attack from former Tory leadership contender Rory Stewart, who accused Downing Street of failing to take the outbreak seriously enough.

“Schools should be shut now. If the government are not prepared to shut them now, they should – at the very least – state clearly and transparently what their triggers will be for closing schools over the next few days. All medium and large gatherings should be cancelled,” he said.

Labour leadership candidate Lisa Nandy urged the government to extend the Brexit transition period beyond December 2020, to deal with the impact of the virus.

“Our businesses and our communities cannot cope with more uncertainty during this pandemic. British companies who trade with the EU do not know what terms they’ll be trading on in 10 months’ time. Add to this the falling demand and disruption created by coronavirus and it is reasonable to expect many businesses will not survive,” she wrote in the Guardian, adding, “This must happen now.” The government has insisted it has no intention to extending the deadline.