The future of the plant was thrown into jeopardy in March when its Chinese owners Jingye said it was no longer financially viable to keep the blast furnaces burning, putting 2,700 jobs at risk.
That led the UK government to pass emergency legislation to prevent the closure of British Steel's main plant in northern Scunthorpe earlier this month.
A new interim management team was also appointed.
British Steel said on Tuesday that "it will not continue with the consultation on redundancies announced by the previous management".
"The work done to secure the raw materials we need for both... blast furnaces means we are able to run both continuously," added interim chief commercial officer Lisa Coulson.
Before the government took control of the company, Jingye had halted orders of raw materials such as coking coal and iron ore, after losing around �700,000 ($937,000) per day on the plant.
The fallout over British Steel also led to a spat with China.
Beijing warned Britain against "politicising" the rescue of British Steel, while UK Business Secretary Jonathan Reynolds said the UK had been "naive" to let the Chinese firm take over part of the sensitive steel industry.
The government is now looking for potential private buyers for the company, although nationalisation remains an option.
The plant in northeast England is the last in the UK to produce virgin steel used in construction and rail transport.
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