GKN Automotive, owned by Melrose, said it had reviewed proposals put forward by Unite to save the factory but the outlook for the sector remained unchanged.
The company announced earlier this year it intended to close the site in 2022, with the loss of more than 500 jobs, transferring work to Europe.
Unite's convenor at the plant, Frank Duffy, said: "This is a deeply disappointing response from GKN Automotive.
"Unite entirely rejects the false notion that there is not a long-term viable future for the factory."
Unite national officer Des Quinn said: "Unite calls on all interested parties including central government, local government, the supply chain, customers and GKN Automotive to come together and ensure the factory's future.
"In order for the electrification of cars to be a success in the UK, it is essential that GKN remains open and full functioning and in order for that to be achieved it needs government support."
A company spokesman said: "GKN Automotive has fully reviewed the counter proposals put forward. However, the outlook for the highly competitive automotive market remains unchanged.
"Regretfully, therefore, we are proceeding with our proposal to close the site. Supporting our people continues to be our priority."
Jack Dromey, Labour MP for Birmingham Erdington, said the decision was "devastating" for the workers, adding: "The workers, supported by Unite, worked tirelessly to produce a comprehensive and detailed alternative plan to closure.
"It is therefore fundamentally wrong that GKN/Melrose have now called time on the consultation process and instead intend to push ahead with closure.
"I will be seeking urgent discussions with the chief executive of GKN and also the Government, who have publicly indicated their commitment to offer support to allow the plant to remain open."