The new offer would have seen workers’ pay increase by £30 a week. The Transport and General Workers’ Union said the offer was rejected by 53% of voters.
A union spokesman said it was disappointed with the result as it had been recommended by a joint negotiation committee of unions and employers.
More than 7,000 staff at the sites in Gaydon and Solihull staged a series of 24-hour strikes in 2004 over pay.
Trade unions will now meet to discuss the next steps.