* New law subsidises renewable energy, bans new nuclear plants
* Law gets 58 percent support in binding referendum
* Critics worry about costs, reliability (Recasts with provisional result, reaction)
By Michael Shields and John Miller
ZURICH, May 21 (Reuters) - Swiss voters backed the government's plan to provide billions of dollars in subsidies for renewable energy, ban new nuclear plants and help bail out struggling utilities in a binding referendum on Sunday.
Provisional final figures showed support at 58.2 percent under the Swiss system of direct democracy, which gives voters final say on major policy issues.
The Swiss initiative mirrors efforts elsewhere in Europe to reduce dependence on nuclear power, partly sparked by Japan's Fukushima disaster in 2011. Germany aims to phase out nuclear power by 2022, while Austria banned it decades ago.
"The results shows the population wants a new energy policy and does not want any new nuclear plants," Energy Minister Doris Leuthard said, adding the law would boost domestic renewable energy, cut fossil fuel use and reduce reliance on foreign supplies.
"The law leads our country into a modern energy future," she told a news conference, adding some parts of the law would take effect in early 2018.
Debate on the "Energy Strategy 2050" law had focused on what customers and taxpayers will pay for the measures and whether a four-fold rise in solar and wind power by 2035, as envisaged in the law, can deliver reliable supplies.
Leuthard has said the package would cost the average family 40 francs more a year, based on a higher grid surcharge to fund renewable subsidies.
Critics said a family of four would pay 3,200 Swiss francs ($3,290) in extra annual costs, while more intermittent wind and solar energy would mean a greater reliance on imported electricity. Switzerland was a net power importer in 2016.
Most parties and environmentalists hailed the result.
"The voting public has ... paved the way for a future that builds on sustainability, renewable energies and energy efficiency. Today's decision is good for the climate, the environment, our jobs, the Swiss economy and the whole population," the Social Democrats said.
The electrical and mechanical engineering sector, which opposed the law, said it was important to see how it is implemented.
"The problem of long-term security of electricity supplies must be resolved. It is also important for companies that the costs and the regulatory burden not swell," it said.
Under the law, 480 million francs will be raised annually from electricity users to fund investment in wind, solar and hydro power. An additional 450 million francs will be set aside from an existing fossil fuels tax to help cut energy use in buildings by 43 percent by 2035 compared with 2000 levels.
Solar and wind now account for less than five percent of Switzerland's energy output, compared with 60 percent for hydro and 35 percent for nuclear. Under the new law, power from solar, wind, biomass and geothermal sources would rise to at least 11,400 gigawatt hours (GWh) by 2035 from 2,831 GWh now.
The law will ban building new nuclear plants. Switzerland has five plants, with the first slated to close in 2019. Voters have not set a firm deadline for the rest, allowing them to run as long as they meet safety standards.
The law also helps utilities that now rely on hydropower, and whose costs exceed Europe's wholesale prices.
Alpiq, BKW, AXPO and other utilities would share a 120 million franc annual subsidy to help close the gap between production costs and market prices. Other funds would help build new dams or refurbish old ones. For a FACTBOX see ($1 = 0.9722 Swiss francs) (Reporting by Michael Shields; Editing by Tom Heneghan)