The ad, which was due to run on stations throughout August, features the voices of soap opera actors advising consumers to 'Think of England'.
The RACC said that the ads contravened guidelines which state that unions are allowed to advertise only services for new members.
The radio ad was due to be the latest instalment in a £1m campaign asking car buyers to snub Peugeot following its decision to close its Ryton factory in the West Midlands.
The two unions have secured 500 poster sites for their campaign, including some near Peugeot dealerships (Marketing, 5 July).
They have also secured spots on the road to the ExCel exhibition centre in London, where the British Motor Show will run from 20-30 July.