The crash occurred on 27 October 2018, about an hour after a home game with West Ham United, when the aircraft took off from the club’s King Power Stadium and crashed shortly after.
Stewarts said High Court action had been launched on Friday.
An inquest into the deaths is set to begin on Monday, more than six years later, with eyewitnesses, emergency service staff and corporate witnesses all set to give evidence in front of a jury.
A report by the Air Accidents Investigation Branch (AAIB), published in September 2023, found the crash was “inevitable” after a sequence of mechanical failures, and said the pilot could have done “very little” to save everyone on board.
Chief inspector of air accidents at the AAIB, Crispin Orr, said Mr Swaffer did what he could to control the Leonardo AW169 helicopter, but the catastrophic failure in a bearing in the tail rotor resulted in the aircraft making a sharp right turn.
As the helicopter – which had reached an altitude of about 430ft (131m) – was turning out of control, a shout of “hey, hey, hey” came from the rear cabin, where Mr Vichai and his employees were seated, the AAIB said.
In aircraft voice recordings, Mr Swaffer was heard to say: “I’ve no idea what’s going on”, shortly before the helicopter crashed into a concrete step.
