By Philip Pullella

ROME (Reuters) - Italy's anti-establishment 5-Star movement, buoyed by big gains in local elections, has pressed demands for a referendum on whether to keep the euro, something that would add to a wave of plebiscites shaking politics across Europe.

The fact that Britain is holding a referendum on whether to remain in the European Union showed the bloc was flawed and Italy needed to rethink its relations to the EU, 5-Star's Luigi Di Maio, vice president of the lower house of parliament, said.

Marine Le Pen, the leader of France's National Front, has said she wants a vote on EU membership.

"All EU countries should have a referendum," she told TF1 television. "The EU is in meltdown, it’s falling apart."

In recent months, the Netherlands has had a referendum on EU-Ukraine ties, and Italy on drilling rights, while Switzerland, which often holds plebiscites, is still at odds with the EU over a 2014 vote forcing the government to impose quotas on migrants from the bloc.

"We want a consultative referendum on the euro," Di Maio said during a talk show.

"The euro as it is today does not work. We either have alternative currencies or a 'Euro 2'."

5-Star has suggested Europe adopt two different currencies, one for the rich north and another for southern countries.

Any referendum on the euro would be merely a test of public opinion because Italian law does not allow such votes to change international treaties. It would also require a lengthy parliamentary procedure to organize and would be highly unlikely unless 5-Star first won power at a national election.

But if it were to eventually produce a popular rejection of the euro it would send a clear signal to the government.

Supporters of 5-Star say Sunday's mayoral election results, where the party won in 19 of the 20 cities that went to a runoff vote, including the capital Rome the northern industrial city Turin, as a possible springboard to national rule.

Its founder Beppe Grillo has also called for a referendum on whether Italy should stay in the European Union.

"We are now waiting for the results of the Brexit referendum. The mere fact that a country like Great Britain is holding a referendum on whether to leave the EU signals the failure of the European Union," Di Maio said.

Last week, Nigel Farage, leader of the pro-Brexit UK Independence Party, said the victory of 5-Star's Virginia Raggi as Rome's first woman mayor, followed by a British vote to leave the EU in Thursday's referendum, would be the start of the disintegration of the EU.

(Writing by Philip Pullella and Andrew Heavens; Additional reporting by Gavin Jones; Editing by Robin Pomeroy)