Contestants on Netflix's Squid Game: The Challenge are seeking compensation for injuries they allegedly suffered on the show, their lawyers said.
Express Solicitors is representing two players who it says "suffered injuries such as hypothermia and nerve damage".
Players competed for a $4.56m (£3.63m) prize on the spin-off show, based on the hit South Korean drama Squid Game.
A show spokesperson said in a statement: "We take the welfare of our contestants extremely seriously."
Studio Lambert, the company who co-produced the show for Netflix, has been contacted for comment.
Express Solicitors claimed the contestants suffered the injuries when "they had to stay motionless for hours in cold temperatures while filming".
Daniel Slade, CEO of the UK firm, said: "Contestants thought they were taking part in something fun and those injured did not expect to suffer as they did.
"Now they have been left with injuries after spending time being stuck in painful stress positions in cold temperatures.
"We have a case where someone complains of hypothermia. One had his hands turn purple from the cold."
The law firm said it has sent letters of claim to Studio Lambert outlining their clients alleged injuries it says were "a result of poor health and safety standards on set".
A letter of claim is a step before legal action - putting a person or organisation on notice court proceedings may be brought against them.
The Green Light, Red Light game sees players run to a line while a 13.7ft (4.2m) doll sings and faces the wall. But players must stand still once the doll rotates its neck to face players.
Those caught moving were eliminated using an automated video system with several adjudicators picking out players that moved.
Stephen Lambert, CEO of Studio Lambert, previously said players who got across the line quickly took two hours to finish the game, but slower players took four or five hours.
"Everybody had been told it was going to be arduous," he said in press materials for the show.
Contestant Lorenzo Nobilio told BBC News last week it took him seven hours to finish the game.
Other contestants complained about the cold conditions in a report by Hollywood trade publication Variety.
A spokesperson for Squid Game: The Challenge said: "No lawsuit has been filed by any of the Squid Game contestants. We take the welfare of our contestants extremely seriously."
The game was filmed at Cardington Studios in Bedford in January.
Last week Mr Lambert told BBC News it took player welfare "terribly seriously".
He said: "Everybody was warm when it was going to be cold, we took all the necessary steps to prepare them for that.
"Yes, a few anonymous people were unhappy about the fact they had been eliminated and it had been a cold, quite long experience.
"But it was no worse than many unscripted shows... when you're giving away a huge prize it is always going to be to clear to us it was going to be a tough show to take part in."
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