In Scunthorpe, where steel has been made for 150 years, 4,000 workers face weeks of uncertainty, amid concerns over the devastating impact the closure of the site would have on the town and wider economy.
Hundreds more work at sites in Lackenby and Skinningrove, while another 20,000 are employed by other firms in the supply chain.
Business Secretary Greg Clark said he wanted to help British Steel more, but state aid rules prevented him from doing so.
Mr Clark said it was a “very worrying time” but “not the end” and the Government now “want to make sure some new partners can take these excellent facilities and the excellent workforce forward.”
And he insisted giving £120m of taxpayers money to Greybull just three weeks ago to cover the cost of carbon-emissions credits was “the right thing to do” as the liability would have remained with the steel-making business, making it impossible for a new buyer to come in.
“By providing that facility of £120m it means it is open to new buyers and it is essential that is the case,” he said.
A statement by the Official Receiver said the company would continue to trade and supply its customers. Staff had been paid and would continue to be employed.
Roy Rickhuss, general secretary of the Community trade union, said: “This news will heap more worries on workers and everyone connected with British Steel but it will also end the uncertainty under Greybull’s ownership and must be seized as an opportunity to look for an alternative future.
“It is vital now that cool heads prevail and all parties focus on saving the jobs.”
Hull and Humber Chamber of Commerce said it would be a “travesty” if British Steel, one of whose biggest customers is Network Rail, was allowed to fail.
A statement said: “We feel it is vital for UK manufacturing that we retain a steel industry and call on the Government to do everything that is required to ensure Scunthorpe continues as a going concern.”
Shadow business secretary Rebecca Long Bailey said: “This is absolutely devastating news for the thousands of workers, their families and the communities in Scunthorpe and Teesside and those throughout the supply chain.
“The Tories’ legacy will once again be industrial decline whilst they endlessly squabble over the European Union.”
Meanwhile a three-year-old tweet came back to haunt Nigel Farage, as opponents reminded him of his prediction that a Remain referendum win would kill off Britain’s steel industry.
In April 2016, the Brexit Party leader wrote: “If we vote to Remain on June 23rd it is the end of the steel industry in the country. Simple as that. We must Leave EU.”
With owners, private equity fund Greybull Capital blaming “Brexit-related issues” Labour MP David Lammy responded: “Simple as that?”
Campaign group Another Europe referenced a cause celebre of Brexiteers, tweeting: “This has aged like a bendy banana left in the sun.”