They are angry that General Motors did not consult the council or UK unions before announcing that production of the Vectra would end with the loss of 2,000 jobs.
They are hoping to enlist Mr Byers' support as part of their campaign to reverse General Motors' decision to cease car production at Luton.
General Motors workers across Europe will stage a day of protest on 25 January which will include industrial action.
Roger Lyons, general secretary of the Manufacturing Science and Finance Union, said: "January 2001 will be the month remembered when European workers refused to be treated like animals by multinational companies."
The action was agreed at a meeting of union officials on the company's European Works Council in Germany.
They are angry that General Motors did not consult the council or UK unions before announcing that production of the Vectra would end with the loss of 2,000 jobs.
Unions have also called on Vauxhall to rethink its decision and on the government to offer help to manufacturing firms.
Officials will travel to Zurich in Switzerland in the New Year to press Mike Burns, president of General Motors Europe, to rethink the future of the Luton factory.
The TUC congratulated unions for not accepting the closure as a "fait accompli.
Strategy call
It called on the government to develop "with the utmost urgency" a strategy which included proposals for the protection of manufacturing across all sectors.
British employment laws mean Vauxhall workers in this country would have to be balloted on industrial action.
But the protests, including strikes, could go ahead without ballots in other European countries including Germany, Belgium and France, according to union officials.
Tony Woodley, chief negotiator for the Transport and General Workers Union, said the European union leaders were making it clear to the company that they could not ignore European law on consulting about redundancies.
"Senior members of the works council have decided to seek co-ordinated action to prevent the closure of any plant."
Mr Woodley said he was delighted with the response of union officials across Europe and the "unjustified" decision to end car production at Luton.