A dam collapse in 2015 at an iron-ore mine run by a firm co-owned by BHP killed 19 people and unleashed a deluge of toxic mud into villages, fields, rainforest, rivers and the ocean.
In November, the High Court in London found BHP "strictly liable" for the disaster, following a mammoth trial that could lead to billions of dollars in damages.
High Court Judge Finola O'Farrell on Monday rejected BHP's application to appeal the ruling, saying it had "no real prospect of success".
Nevertheless, BHP said it would still take its case to the Court of Appeal.
"BHP will continue to robustly defend the remaining phases of this action," a spokesperson added in a statement.
The victims first filed a UK legal action in 2018 demanding compensation from BHP. At the time of the disaster, one of BHP's global headquarters was in Britain.
The eventual trial at the High Court ran from October 2024 to March 2025.
A second phase of the case is scheduled to begin in October to determine the amount of compensation to be paid to victims.
The 620,000 claimants are seeking around �36 billion ($48 billion) in compensation, according to a previous estimate from law firm Pogust Goodhead.
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