The cross-Channel rail service has been hit hard by travel restrictions - last year announcing services would not be stopping at the international stations in Ashford and Ebbsfleet until 2022.
Its services from London to the Continent have been slashed to just two a day.
Now the RMT union has formally launched its Save Eurostar campaign to save the service from financial collapse and protect the thousands of jobs which rely on it.
The union says any such collapse would be "disastrous".
A Eurostar spokesman has previously said there is a "real risk to the survival of Eurostar" and that the current situation it faces is "very serious".
The RMT says it will be stepping up political campaigning and pressure and has launched a petition aimed at Transport Secretary Grant Shapps.
It said: "The RMT is calling on the Secretary of State for Transport to urgently agree assistance for Eurostar, which, like other transport operators, has been significantly impacted by the Covid-19 outbreak, but which has not yet received any support from the UK government.
“Like other rail companies and transport operators, Eurostar has been significantly impacted by the ongoing Covid-19 pandemic, with passenger numbers and revenue at a fraction of pre-Covid levels.
“The Eurostar provides a vital, low carbon, link between the UK and mainland Europe, and will be essential to the UK’s green economic recovery from Covid-19. Eurostar is a UK-registered company with its head office in London and the company supports over 3,000 UK jobs. It would be disastrous, economically and environmentally, if the service were not protected.
“Eurostar is part owned by the French state-owned operator SNCF, and it has received over £200m in support from shareholders during the pandemic. However, given that it is likely to be some time before passenger numbers return to pre-Covid levels, it needs further assistance to ensure it can survive during the pandemic.
“Unlike other transport operators, including airlines, Eurostar has not yet received any Covid-19 state support from the UK government.
“RMT is calling on the UK government to urgently agree to work with Eurostar and engage in coordinated action to protect the collapse of this vital transport link and ensure that thousands of UK jobs are protected.”
RMT general secretary Mick Cash added: "Nobody should be under any doubt that the future of Eurostar, and the thousands of jobs that it supports, is threatened by the current stand off.
“It is essential that governments, including the British government, make the emergency funding available to bridge a way through this current lockdown and ensure that Eurostar is there, fighting fit, to help the economy punch its way out of this crisis and provide the essential green rail links to the continent. “
The Department for Transport says its "recognises the significant financial challenges facing Eurostar" and says it has "engaged extensively" with the company and will continue to do so as "we support the safe restart and recovery of international travel".