The government will bring forward emergency legislation to protect private renters from eviction, Boris Johnson has said.
Tenants were "worried sick" they might not be able to pay rents if they fell ill, Labour leader Jeremy Corbyn said at Prime Minister's Questions.
As Wales and Scotland said they would close schools by Friday Mr Johnson said a decision on England was imminent.
It came after Chancellor Rishi Sunak announced £350bn of help for companies.
On Tuesday, the chancellor promised mortgage "holidays", £330bn in loans and £20bn in other aid.
The government had been urged to do more for families, workers and tenants affected by coronavirus.
Mr Corbyn urged the PM to protect private renters in "the interests of public health", adding Britain's 20m private renters were "worried sick" about missing payments if they became ill, lost pay or had to self-isolate.
Mr Johnson said it will bring forward legislation to protect private renters from eviction, but will also avoid "pass[ing] on the problem" by "taking steps to protect other actors in the economy".
Housing associations will not evict tenants who are affected by the virus and fall behind on rent payments, Kate Henderson, of the National Housing Federation, which represents housing associations in England, has confirmed.
Paying tribute to the efforts of teachers, and school staff, Mr Johnson said he wanted to do more to "remove burdens on schools".
He added: "The House should expect further decisions to be taken imminently on schools and how to be sure we square the circle, making sure we stop spread of the disease but relieve pressure on the NHS."
Meanwhile, all schools in Wales will close by Friday at the latest in response to the coronavirus outbreak, the Welsh Government has announced.
Scotland's schools and nurseries will close from the end of this week and may not reopen before the summer, First Minister Nicola Sturgeon has said.
It comes as:
- The total number of positive cases in the UK has risen to 2,626, up from 1,950 on Tuesday, according to government figures.
- The PM will chair a Cobra meeting on Wednesday afternoon before his daily press conference, and the government's scientific advisory group for emergencies (Sage) will meet to discuss the latest information on the spread of the virus.
- A prisoner at HMP Manchester tested positive for Covid-19, the Prison Service confirmed, with 13 prisoners and four staff members being put into isolation as a precaution.
- Supermarkets brought in strict limits on purchases
- Firms thinking of firing staff due to the coronavirus crisis should consider the support available to them first, the new Bank of England boss, Andrew Bailey, has said.
- In the UK, 71 people with coronavirus have died
- Honda will close its Swindon manufacturing plant from the end of Wednesday until at least April 6 to protect staff and because of supply problems caused by the outbreak
- European Union countries have begun turning away travellers from outside the bloc
- The Queen's granddaughter, Princess Beatrice is "reviewing" arrangements for her wedding to Edoardo Mapelli Mozzi on May 29
- Britons in Spain have been urged by the Foreign Office to return before March 24, when all Spanish hotels close
- Share prices fell in Europe and Asia as stimulus packages failed to reassure markets
- The World Health Organization said South East Asian countries must "act now" to tackle the virus
- There are about 200,000 cases worldwide and nearly 8,000 people have died
- Prof Neil Ferguson, who has been advising the UK government on its response to the outbreak and was in Downing Street earlier this week, tweeted that he was self-isolating after developing coronavirus symptoms
- This year's Eurovision Song Contest, which was due to be held in Rotterdam, in the Netherlands, will no longer take place due to the coronavirus outbreak.
- The BBC put filming of EastEnders on hold and Glastonbury Festival was postponed.
In the UK, supermarkets continued to introduce measures to try to stop customers stockpiling and ensure vulnerable people had food during the crisis.
Sainsbury's said it would prioritise elderly and other vulnerable people for online deliveries, as both Sainsbury's and Asda limited people to buying no more than three of any food item.
Other retailers including Tesco and Boots have set limits on particularly popular products including pasta, tissues and hand sanitiser.
Meanwhile, lorry drivers transporting essential goods to supermarkets will be allowed to stay on the road longer without a break after Transport Secretary Grant Shapps temporarily relaxed the rules.
In entertainment, EastEnders will be broadcast just twice a week - rather than four times - as the BBC postponed filming of the soap opera and other dramas "until further notice"
And Glastonbury Festival has been postponed from June 2020 until 2021, its organisers said.
Elsewhere, car manufacturers were among the latest companies to be affected, with Toyota and BMW both suspending production at their UK factories. Toyota employs more than 3,200 people in the UK, while BMW has 6,000 manufacturing staff.
Unveiling the financial measures at a press conference on Tuesday, Chancellor Rishi Sunak said the £330bn in loans - equivalent to 15% of GDP - would be available from next week to help businesses pay for supplies, rent and salaries.
Rachel Reeves, Labour chairwoman of the Commons Business Committee, said there was nothing in the chancellor's announcement to offer financial support to people who were already on statutory sick pay, self-isolating or had been laid off.
And unions raised concerns there were no measures to help freelancers and people working in the gig economy.
The additional measures came after the public were told to avoid all non-essential contact and travel.
By next weekend, those with the most serious health conditions must be "largely shielded from social contact for around 12 weeks", under the latest government guidance.
Testing procedure 'alarming'
Some doctors have called for more testing for the virus among NHS workers to prevent any unnecessary absences.
Speaking at PMQs, Mr Johnson said testing for the virus is to be ramped up to 25,000 tests a day, following criticism too few were being carried out.
The testing will be more than doubled in England, after a prior government commitment to boost tests from 2,000 to 10,000 a day.
Commercial equipment will be brought in to boost the capacity currently available in the NHS and via Public Health England.
Mr Johnson also confirmed that the UK is getting "much closer" to having a generally available test to determine whether someone has had coronavirus.
He added the government is making a "massive effort" to ensure healthcare staff have enough protective equipment to wear while treating patients.
Leading scientists at Porton Down, the Ministry of Defence's highly secure research laboratory in Wiltshire, have been called in to help deal with the spread of coronavirus, the BBC has been told.
A team of about 10 defence scientists are working with public health officials to analyse the spread of the virus and to help with testing.
A man in his 40s with motor neurone disease (MND) is thought to be the youngest person in the UK to have died having tested positive for coronavirus.
Craig Ruston, understood to be 45, died in Kettering, Northamptonshire, on Monday morning and his chest infection was diagnosed as Covid-19.
The government's chief scientific adviser Sir Patrick Vallance said it would be a "good outcome" for the UK if the number of deaths from the virus could be kept below 20,000.
Some 2,626 people have tested positive for the virus in the UK, according to the latest Department of Health figures - but the actual number of cases could be as high as 55,000.
As of 9am on Wednesday, a total of 56,221 people have been tested, 53,595 of whom have come back as negative.
Among the latest confirmed cases is a newborn baby at James Paget hospital in Norfolk.
In other UK developments:
- Parkrun, which organises 5km weekly runs around the world, has suspended its 675 events in the UK until at least the end of March
- Department store chain Selfridges is closing its London, Birmingham and Manchester stores from 19:00 GMT on Wednesday
- The United Synagogue - the biggest group of synagogues in the UK - has closed all of its synagogues until further notice
- British-Iranian charity worker Nazanin Zaghari-Ratcliffe has been temporarily released from prison in Iran because of the outbreak. She will be required to remain within 300m (984ft) of her parents' home in Tehran
- All non-urgent operations in England and Scotland will be postponed from 15 April for at least three months to free up beds for virus patients
- The Foreign Office advised British nationals to avoid all non-essential foreign travel for at least 30 days
- No new Crown Court trials will take place in England and Wales if they are expected to last longer than three days
- The government set out emergency legislation, which would give police the powers to arrest and isolate people to protect public health
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