Scottish voters want a Labour government at Westminster dependent on SNP support, according to Scotland’s first minister, Nicola Sturgeon.

Having a minority Labour government reliant on SNP votes, rather than a majority one, would lead to better decisions for Scotland, but also “more progressive decisions for the whole of the UK”, she said on Sunday.

Sturgeon told the BBC’s Andrew Marr show that the Westminster establishment “really needs some progressive forces at its heart” and that she wanted to see SNP MPs “being a constructive and progressive force in the House of Commons”, making alliances with parties such as Plaid Cymru, the Welsh nationalists and the Greens.

“If you look at polls in Scotland, as well as showing a substantial SNP lead they show that the most popular outcome in Scotland in the general election is a Labour government dependent on SNP support,” she said.

With one poll last week suggesting the SNP could be on course to win as many as 55 of the country’s 59 seats, Sturgeon cited Trident nuclear weapons programme as an example of an area where the party would push for progressive policies at Westminster.

The SNP says that the cost of Trident renewal would be £3bn a year, rising to £4bn in the 2020s, and Sturgeon said her party would be urging Labour to abandon its support for nuclear weapons, and to invest the money instead in health and education.

She also said the SNP would be pushing for “full fiscal autonomy” for the Scottish government, not just the devolution plans in the Smith commission report, which, she said, would leave 70% of tax powers and 85% of the social security budget in the hands of Westminster.

She reaffirmed the SNP’s commitment not to support a Conservative government at Westminster, saying that SNP votes would not prop up a Tory administration either formally or informally.

And she confirmed that, although the SNP would not vote on “purely English matters” at Westminster, they would vote on English health laws, because health spending decisions would have “a direct knock-on effect for Scotland’s budget”.

In the past, some SNP figures have argued that Scotland would not necessarily need a second referendum to become independent and that another mechanism, such as the election of a second majority SNP government at Holyrood in 2016, could lead to Scotland breaking away from the UK.

But Sturgeon firmly rejected this notion. “The only way for Scotland to become independent is for a majority of people in Scotland to vote for independence in a referendum – that is the route to independence,” she said.