The Transport and General Workers Union will be handing out leaflets to Peugeot customers and the general public in Rugby and Leicester today at lunch and tomorrow morning.
The T&G also confirmed that a ballot for industrial action will also start today and conclude on June 5.
The decision to close the plant was made in April, with a loss of approximately 2,300 staff.
The plant will be brought to a close in two stages. It currently operates two shifts, which will be moved to a single shift in July. Production will not continue beyond July next year.
The company says it will work with trade unions and the Government throughout the next few months to provide support packages for its staff.