Tony Woodley, general secretary of the Transport and General Workers Union, has written to the chairman of the Trade and Industry Select Committee to protest against the job losses at the plant in Browns Lane.
Mr Woodley, whose union represents many of the 1,150 workers who are set to lose their jobs, told Martin O'Neill that an inquiry was "both desirable and necessary".
Pointing out that Ford gave evidence to the Select Committee earlier this year, Woodley noted Ford presented an "upbeat" picture of their performance.
Woodley argued that Ford's announcement on September 17 to end car production at Browns Lane constituted new evidence, and therefore the committee should be recalled to quiz Ford bosses.
O'Neill has already indicated that he has written to the company himself seeking an explanation. Once he receives a reply, Mr O'Neill has said he intends to meet with the Committee.
In his letter, Woodley says: "As chairman of the Select Committee you will know that the implication for manufacturing, the UK economy and employment not only in vehicle manufacturing but also in the supply chain and the service sector which are dependent on the automotive industry, are extremely serious indeed. The company's announcement did not form part of their original evidence and is therefore new evidence. I write requesting that the Select Committee be reconvened urgently on the matter of Jaguar cars."