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UPDATE 3-Greens surge in Swiss election as climate change worries come to the fore

By Marina Depetris and Cecile Mantovani

* Right-wing People's Party loses share but keeps lead

* Greens surpass centre-right Christian Democrats for first time

* Greens leader eyes first cabinet seat for party (Adds latest projections, party comments)

By Marina Depetris and Cecile Mantovani

BERN, Oct 20 (Reuters) - Support for the Greens surged in Switzerland's election on Sunday, moving politics to the left and putting environmentalists in the mix for a seat in the broad coalition that has governed the country for decades.

The far-right Swiss People's Party (SVP) remained in first place, according to projections after the parliamentary election, but like other big parties lost ground as environmentalist parties seized on voters' concerns about climate change to shake up the political establishment.

"It is not a green wave, it is a tsunami, a hurricane," Celine Vara, deputy Greens leader who won a seat in the upper house of parliament for Neuchatel canton, told Swiss radio.

Far from the sea, Switzerland is especially vulnerable to climate change as temperatures in the country are rising twice as quickly as the global average.

"I think it is pretty obvious that is the most important topic of all in our time and age. There is really not any time to lose," said Anja, a 25-year-old psychology student, who gave only her first name at a Bern polling station.

The SVP, which won a record number of seats in 2015 amid Europe's refugee crisis, slipped 3.6 points to 25.8% while the Greens' share surged 5.9 points to 13.0% of the vote for the lower house, according to a gfs.bern projection for broadcaster SRF.

The smaller, more centrist Green Liberal Party (GLP) advanced to 7.9%, bringing the two parties' combined strength to nearly 21% should they overcome policy differences and decide to join forces.

Together they gained 26 seats in the 200-seat lower house, potentially putting them in line to take one of the seats in the seven-seat cabinet, the Federal Council.

Changing just one member of the cabinet would be a political sensation. The Greens have never had a seat in the federal government.

The centre-left Social Democrats remained second on 16.6% and the centre-right Liberals (FDP) third at 15.3%, but the Greens leapfrogged the centrist Christian Democrats (CVP), which has one seat on the Federal Council.

Cabinet seats have been divvied up among the SVP, SP, FDP and CVP in nearly the same way since 1959. The three biggest parties get two seats and the fourth-biggest gets one under the informal "magic formula" system.

"The Federal Council in its current composition no longer fits (the changed political situation)," Greens leader Regula Rytz told Swiss TV, suggesting the party could seek to wrest a cabinet seat from the FDP.

In December, the two parliamentary chambers will elect the government. In the past it has taken more than one national election cycle for that selection procedure to change the cabinet lineup to more closely reflect the results of voting.

The election of two new cabinet members after resignations last year also complicates the matter for the Greens by making it necessary to vote out a sitting member, an unusual step.

The election campaign was light on typical hot-button issues such as migration and Swiss ties with the European Union that have given the anti-EU SVP a boost in the past.

Switzerland's system of direct democracy gives voters a final say on major issues decided by referendum. (Writing by Michael Shields, Additional reporting by Stephanie Nebehay and Emma Farge Edition by Dale Hudson and Susan Fenton)