Two major financial players are suing the London Metal Exchange for a total of nearly half a billion dollars, after the exchange earlier this year suspended nickel trading and canceled some trades following wild swings in the metal’s price.

The activist hedge-fund manager Elliott Management Corp. is seeking more than $456 million, while the market maker Jane Street Group LLC is claiming about $15.3 million, according to Hong Kong Exchanges & Clearing Ltd. , which owns LME. The lawsuits are a fresh headache for the LME, whose actions had already drawn criticism from some market participants and prompted a review by British financial regulators.

The two companies are challenging the exchange’s decision to cancel trades that they say they made early on March 8, HKEX said in separate statements Monday and Tuesday in Hong Kong. Elliott and Jane Street filed their cases separately in the English High Court.

“The LME management is of the view that the claim is without merit and the LME will contest it vigorously,” HKEX said of both suits.

An Elliott spokesperson confirmed that the firm started legal proceedings against the LME. By canceling trades, the LME either exceeded its authority or was acting “unreasonably and irrationally,” the spokesperson said.

Jane Street took the legal effort “to recoup its losses caused by the LME’s illegal actions and to strengthen the exchange and restore the market’s trust in it,” a spokesman for Jane Street said. “The LME’s arbitrary decision to cancel nickel trades during a period of heightened volatility severely undermines the integrity of the markets and sets a dangerous precedent that calls future contracts into question,” he said.

Elliott and Jane Street argue the metal exchange’s action “was unlawful on public law grounds and/or constituted a violation of the claimants’ human rights,” HKEX said.

Elliott, founded by billionaire Paul Singer, brought the case through two vehicles, Elliott Associates LP and Elliott International LP. Jane Street is pursuing the case through its subsidiary Jane Street Global Trading LLC. The claims are being pursued as a judicial review, a proceeding in which a judge assesses the legality of a decision or action taken by a public body.

Russia’s invasion of Ukraine sparked sharp gains in many commodities. The nickel market proved particularly turbulent because the price moves upended a massive trade against the metal by Tsingshan Holding Group, a Chinese nickel producer.

The LME stopped nickel trading early on March 8 and retrospectively canceled trades in the eight hours before the suspension. It was the first time the LME had frozen trading for a metal since the collapse of an international tin cartel in 1985 and the 145-year-old exchange came under criticism from traders for the way it handled the crisis.

The LME’s decision to cancel trades roiled hedge funds that felt the exchange violated a solemn rule that trades should never be canceled. Other market players could also target the LME with legal action.

“There are a lot of eyes on this case. There are a lot of investors out there who will be interested in putting a claim forward. Trading on that day was sizable,” said Ashraf El-Ansary, managing partner at Principa Capital, a London-based macro hedge fund.

Principa stopped trading on the LME after the exchange canceled its nickel trades in March, he said.

U.K. financial regulators in April launched a review into the breakdown in nickel trading. The Financial Conduct Authority and the Bank of England said they would look for ways that the LME can improve its governance, market oversight and risk management.

In late April, the exchange’s parent said LME Chief Executive Matthew Chamberlain would remain in his position, reversing an earlier plan to depart.

HKEX shares rose 1.6% Monday in Hong Kong, underperforming a 2.7% increase for the Hang Seng Index.

—Anna Hirtenstein contributed to this article.

Write to Dave Sebastian at dave.sebastian@wsj.com