Support for Scottish independence has hit the highest level since Alex Salmond won office over four years ago, but a larger number of Scots favour more power within the UK, a study has found.

The Scottish social attitudes survey, regarded as one of the most authoritative tests of public opinion, has identified a marked shift in support towards greatly increasing Scotland's powers on a range of questions in the past year.

But it also shows that public support for independence is heavily dependent on whether it would improve prosperity and economic success, suggesting that for many Scots independence is not based on a principled belief in national sovereignty for its own sake.

Published on Monday, the annual study by the Scottish Centre for Social Research found that nearly a third, 32%, of Scots supported independence this year compared with just 23% last year – a rise likely to be closely linked to Salmond's landslide victory in May's elections for the devolved parliament.

That is the highest figure since Salmond and the Scottish National party narrowly won power at the 2007 elections to Holyrood but it remains lower than the highest figure the social attitudes survey has found so far of 35% in 2005.

Asked whether they would support independence if everyone was £500 better off, 29% said they were "strongly in favour" and 36% said they would be "in favour".

But in one of the most significant findings, the survey has confirmed that the major battle ground for reformists is in increasing the Scottish parliament's powers while remaining in the UK, a move slowly winning political support.

Salmond has confirmed he would like the independence referendum, due to be held in 2014 or 2015, to have a second question on whether to increase devolution but only if another party or non-party based campaign can lead and fund that campaign.

The study found 58% of Scots wanted to keep Holyrood and Westminster, sharing power and responsibility, a figure which is again close to previous studies. A third of those backing independence also want Scotland to leave the European Union.

But more detailed questioning confirmed a shift towards much greater powers for Holyrood: 43% preferred Holyrood to have greater autonomy within the UK, an agenda being heavily influenced by Salmond's demands for Holyrood to immediately gain control over corporation tax, the Crown Estates, borrowing and excise duties.

Further questioning found that 29% of Scots believe Holyrood should control every aspect of Scotland's domestic affairs, including all areas of taxation, and just leave defence and foreign affairs to Westminster, a position often known as "devolution max", or "devo max".

Only 21% support the current devolution settlement, under which Westminster controls welfare, social security, the overall taxation system, defence, foreign affairs and European affairs.

But more worryingly for Salmond and the SNP, given the euro crisis and the global recession, the state of the economy has emerged as a very significant influence on attitudes.

John Curtice, the voting expert who led the survey, said: "The appetite for a more powerful parliament, including independence, has grown in the last 12 months. However, support for independence is still no higher than it has been on previous occasions since the advent of devolution.

"If the SNP are to persuade a majority of Scots to back independence they will need to convince them of the economic case for leaving the union – and that is a debate that is still to be won or lost."

Although 34% of the 1,197 people questioned said Scotland's economy would be "a lot/a little" better, outweighing the 29% who said it would get worse, 46% said they would be "very/quite worried" about an independent Scotland's future.

The number of people who said they would support independence more than halved, dropping from 47% to 21%, if the economy would get worse as a result and leave Scots £500 a year worse off. Although Scots nationalists argue that taking control of North Sea oil would boost the economy, many economists believe the industry is too volatile to underpin government spending.

The findings will be very closely studied by the pro-UK parties and pro-devolution campaigners.

The survey boosts the position taken by the thinktank Reform Scotland, which has published a less radical proposal known as "devo plus" to give Holyrood control over 64% of its tax revenues and welfare policy. It would support a two-question referendum and is the body most likely to become involved in a second question campaign.

However, the findings will be a further challenge to the pro-UK parties. The official position of the Tories and Liberal Democrats is to resist any pressure for extra powers until new measures under the Scotland bill, chiefly to give Holyrood control over basic income tax rates, come into force.

This month, Douglas Alexander, the shadow foreign secretary and the most influential Scot in the Labour shadow cabinet, said Labour needed to draft policies to strengthen Holyrood's powers, in a marked shift in party policy.

The Scottish Liberal Democrats have launched a commission on "home rule" under the former party leader Menzies Campbell, while several senior ex-Labour ministers, including Henry McLeish and Malcolm Chisholm, have openly backed "devo plus".

• This article was amended on 14 December 2011. The original sub-heading said: Nearly a third of Scots in favour of increasing Scotland's powers but support dependent on whether it would improve prosperity.