All retailers will be receiving guidance about the change, which will be kept under review, Burnham told the BBC.
He also said some of the wildfires burning across the country will have been started by disposable barbecues.
Speaking to BBC Radio 5 Live’s Matt Chorley, the prime minister said: “We’ve got 37 fires across England and Wales right now, four of them are major incidents.”
He added: “We’re going into a difficult weekend, please just think about the situation that we’re in.
“Britain is a tinderbox right now. Setting a fire in any outdoor setting of any kind is a risk to other people’s homes, it’s a risk to other people’s lives, don’t do it, please don’t do it.”
Many large retailers and supermarkets had already voluntarily stopped selling the devices under a framework agreed in 2023, external between fire chiefs and the British Retail Consortium.
It said that retailers should suspend sales once an extreme heat event has been declared as imminent, or in response to “reasonable, evidence based” requests from local councils.
