It comes after business secretary Vince Cable exclusively told the Daily Echo he had been kept in the dark about Ford's plans to close the Swaythling plant plan when £10m of Government funding for the motor giant was signed off just days earlier.
Ford said today an earlier briefing of government officials would not have been “possible or appropriate”.
More than 500 staff now face the axe under plans to close the plant next July to cut costs amid a slump in European car sales.
Roger Maddison, Unite’s national officer for the automotive industry at Unite, said a mass meeting of union officials at the Southampton plant had today reached a "unanimous decision" to oppose the closure and warned strike action had not been ruled out.
The union will hold a further strategy meeting in London tomorrow before consulting Ford workers on what action, if any, to take.
Dr Cable told the Echo if ministers had been aware of last Thursday's closure announcement earlier the Government would have gone back to Ford and asked “what on earth was going on”.
He said he felt “let down” Ford had not given more notice of the closure announcement.
The Government has earmarked a £10m grant to Ford through the Regional Growth Fund.
A Ford spokesman said: “Ford's planned European restructuring actions, including those affecting Southampton and Dagenham, were approved by the board of Ford Motor Company shortly before the start of communications with employees and employee representatives, and therefore an earlier briefing of government officials would not have been possible, or appropriate.
“The offer of the grant is a conditional one, that is not yet confirmed, and it would relate to Ford's significant planned investment in powertrain manufacturing and engineering in the UK, which includes the announcement to add a new next-generation, low-CO2, 2.0-litre diesel engine in Dagenham.”