The four charities run a total of more than 2,000 shops in the UK.
Save the Children, which has 126 charity shops, closed all its shops yesterday saying they would remain shut “until the danger from coronavirus has passed”.
Oxfam said its almost 600 stores would be closed from Saturday “until the heightened danger posed by the coronavirus has passed”.
The 600 stores run by CRUK shut at 4pm today in London and the rest will close from 4pm tomorrow nationwide to stem the spread of the virus.
And the BHF will close its 750 stores for two weeks from today to protect staff, customers and volunteers from Covid-19.
Save the Children UK has about 3,500 volunteers working in its shops. The charity said many of these were elderly, the section of the population most at risk from Covid-19.
Seventy employees are being asked to work from home on full pay, the charity said.
The closures would cost the charity £900,000 a month in income, it said.
Fifty-three shops run by the charity were unable to open yesterday after volunteers opted to remain at home.
Ian Matthews, trade director at Save the Children UK, said: “The past few days have been some of the most difficult and surreal times any of us will have faced in both our personal and professional lives.
“Yet it has also demonstrated some extraordinary teamwork, collaboration, commitment and passion for Save The Children, all qualities that will enable us to work through these uncertain times while we prepare for re-opening when possible.
“We’re taking this step to help volunteers stay safe and I want to thank every one of them for their dedication.”
Oxfam said its decision to close its shops was primarily to protect the health of its staff, volunteers and customers.
There are about 20,000 volunteers working at Oxfam’s shops, normally assisted by one or two staff per shop.
Oxfam shops raised £17.3m in the year to 31 March 2019, contributing £1.4m a month to the charity.
The Oxfam Online Shop would remain open, the charity said.
Anne Webb, deputy trading director at Oxfam, said: “It is with a heavy heart that we have decided to shut our shops until the danger of the coronavirus has eased.
“But it’s absolutely the right thing to do because the safety of our staff, volunteers and shoppers comes first. Some of our volunteers are elderly and especially vulnerable to the infection, and we are acutely conscious of our responsibilities towards them.”
The BHF said it would be unable to receive donations after today, but said its eBay store was still in operation.
Allison Swaine-Hughes, retail director at the British Heart Foundation, said: "As significant numbers of our volunteers, staff, customers and donors are in high-risk groups or are directly affected by heart and circulatory disease, it’s only right that we close our 750 shops and stores. Without the invaluable contributions of our staff and volunteers, it is not possible for us to operate normally.
“As a result of this decision, all of our collection services have been suspended with immediate effect and we would ask that people do not leave donations outside BHF shops because we will have no way of collecting them in the coming weeks.
“We hope to re-open all shops as soon as it is safe to do so.”
Michelle Mitchell, chief executive of Cancer Research UK, said: “We are planning for different scenarios and will do all we possibly can to ensure that our life-saving work continues. But with that come difficult decisions and today we have opted to close all 600 of our stores across the UK.
“Over the past fortnight our shops have raised £2.4m to help fund vital cancer research, which is an incredible achievement in exceptional times.
"However, the chain relies on the unswerving support of thousands of dedicated volunteers and customers, many of whom are older people, and ensuring their wellbeing is paramount."
The charity's online shop and eBay site will remain running, the charity confirmed.
Mitchell said the charity was reviewing its events portfolio, including Race for Life, in the wake of the spread of Covid-19.