Danes came out in droves Thursday to vote in a general election expected to bring the centre-left back to power after a decade in opposition and deliver the country's first woman prime minister.

Polls have consistently suggested that Helle Thorning-Schmidt, 44, who heads the Social Democrats and a broad centre-left coalition, is likely to turf current Prime Minister Lars Loekke Rasmussen, 47, out of office.

Thorning-Schmidt, the daughter-in-law of British Labour politician Neil Kinnock, has vowed to shore up Denmark's welfare state and stimulate its slumping economy with spending, in contrast to the austerity measures proposed by Rasmussen.

A loss for the coalition government, made up of Rasmussen's Liberal Party and the Conservative Party, would also end the powerful influence wielded by the populist, anti-immigration Danish People's Party (DPP).

For 10 years, the DPP has pressured the centre-right coalition to adopt some of Euorpe's most draconian immigration and integration regulations, in exchange for its support on other issues in parliament.

Under a clear blue sky, long lines stretched outside the polling station in the working-class Copenhagen neighbourhood of Valby, as many voters cast their ballots early before heading to work.

One of them was Rukshana, a 50-year-old daycare worker who did not want to give her last name.

"I'm voting for the red bloc (centre-left), because they are good for the Danish population. We have had enough of (DPP leader) Pia Kjaersgaard," she said.

"This has been the worst 10 years for integration... I know a lot of families, whose child was born in Denmark, but the mother or father cannot be with their children" because of the strict immigration rules, said Rukshana, a Danish citizen of Pakistani origin.

While she touched on the once-heated issue of immigration, the election campaign primarily focused on how to stir the country out of the slump caused by the global financial crisis.

A slew of polls handed the left-leaning opposition, made up of the Social Democrats, Social Liberals, Socialist People's Party and Red Greens a clear lead over the government and its parliamentary supporters, the DPP, the Christian Democrats and the Liberal Alliance.

While showing a narrowing gap between the blocs compared to polls in recent days, none have shown the current government leading the pack.

They indicated that the centre-left would win between 90 and 92 seats in Denmark's 179-seat parliament, against between 83 and 85 seats for the centre-right. Denmark's autonomous territories Greenland and the Faroe Islands hold two seats each.

In the last election in 2007, the centre-right government and its allies took 94 seats against 81 for the centre-left opposition.

Rasmussen however insisted he was not ready to give up.

"I will be on the campaign trail until the polling booths close," he told AFP after casting his vote at the small hamlet of Graested, some 40 kilometres (25 miles) north of Copenhagen, covered in campaign posters showing his smiling face.

The clearly pro-Rasmussen village even sported a whiteboard offering "50 percent off on your next car service if you vote for Lars".

A Voxmeter poll for the Ritzau news agency showed Thorning-Schmidt was by far the preferred candidate to head the next government, with 48 percent overall backing her, and a full 59.7 percent of women questioned saying she would make the best prime minister.

Rasmussen meanwhile received 45.2-percent overall backing in that poll.

Some four million Danes were eligible to cast their ballots before polling stations close at 8:00 pm (1800 GMT), with voter turnout expected to be high.

In 2007, more than 86.5 percent of eligible voters cast their ballots.