Mr Andrew, a former England international and Newcastle's director of rugby, accused Gloucester's French hooker Olivier Azam of racially abusing Newcastle's Tongan flanker Epi Taione during a league match last month.
But Gloucester chairman Mr Walkinshaw claimed the “appalling charges” of racism were not true and banned Mr Andrew from Kingsholm.
The Rugby Football Union called Mr Walkinshaw's stance unacceptable and said it was against the rules of the game.
It intends to investigate the allegation of racism after holding a disciplinary tribunal yesterday. Both Mr Azam and Mr Taione, who received red cards during the game, have been suspended.
TWR, set up in 1975, is a £300m turnover company that specialises in vehicle design, engineering and manufacturing in the motor industry. Projects range from design only or performance enhancements, to complete engine or new vehicle engineering production. TWR has undertaken a number of projects for manufacturers like BMW, Jaguar, Rover and Volvo, preparing cars for race events.
Mr Walkinshaw is also chairman and team principal of the Formula 1 Arrows team.