The French carmaker announced in April that it was moving production to Slovakia and France and closing the Coventry factory.
Workers’ unions TGWU and Amicus have already called for boycotts of Peugeot and its sister company Citroën.
GMB general secretary Paul Kenny said: ‘The GMB will be removing Peugeot from our list of approved tenderers when our fleet car scheme shortly comes up for review.
‘We shall also be bringing to the attention of our regions and branches the importance of considering ethical car purchase, to look at the facts of the Peugeot closure and the redundancies of 2,000 people in Coventry before making their next car purchase.’
A spokeswoman for Peugeot’s parent company PSA said Peugeot had not supplied any vehicles to GMB, or to the other unions boycotting the firm.
She said: ‘PSA Peugeot Citroën disagrees with the principle of the unions’ call for a boycott and believes there is no justification for these measures, particularly given the decisive vote against industrial action by union members at Ryton on June 5.
‘The campaign only seeks to put at risk the jobs of the 5,000 PSA Peugeot Citroën staff who will continue to be employed in the UK after the closure of the Ryton plant.’
She added: ‘We do not believe the unions’ boycott will work and continue to focus our efforts on helping our employees at Ryton back into employment, with an investment of £5 million on retraining and advisory services as well as strong financial packages that have already been taken up by a number of our employees.’