A strong majority across the UK favours keeping the kingdom united, according to a new Guardian/ICM poll. But as Scotland's first minister Alex Salmond prepares to publish his plans for an independence referendum this week, there are very different ideas in England and Scotland about whether it should be for the whole of Britain or for Scots alone to seal the union's fate.

Some 68% of respondents across Britain say "the UK is stronger together", as against just 24% who believe England and Scotland "are proud nations in their own right", which could thrive on their own.

The unionist balance of opinion is evident across England, as well as Scotland and Wales. The pro-UK majority exceeds two to one in every case, even among Scots who back the union on this question by a 63%-30% margin. The Scotland-only results necessarily rely on a much smaller sample, but are in line with the findings of other recent polls in suggesting that Salmond has a mountain to climb.

A recent YouGov survey of Scottish voters for Channel 4 news pointed to a 61%-39% referendum defeat for independence.

David Cameron started the political year by demanding the Scottish government set out how the referendum would be run, but he ran into a furious reaction from the SNP administration at Holyrood, which accused him of trying to dictate the terms and the timing from London. Cameron's involvement wins some support from voters – and in Scotland as well as England.

Across Britain as a whole, only 28% deem that "it is for the Scottish government to manage Scotland's referendum" as against 61% who judge that London is right to want "a say on the ground rules" because "independence would affect the whole UK".

Even among Scottish respondents, a majority, 56%, take the latter position, against just 39% who think that the plebiscite is Scotland's to manage alone. Over the weekend it appeared London and Edinburgh were inching closer on the referendum's management, with reports that Holyrood can accept the involvement of the UK-wide electoral commission, so long as it is subjected to Scottish oversight.

But if the poll points to compromise over how the referendum is managed, there are sharp differences between the Scots and the English when it comes to who should get to take part. A clear majority of Scottish respondents, some 55%, believe that in or out of the UK, "Scotland's future is a matter for the Scottish people alone". By contrast, two-thirds of voters in both England (66%) and Wales (65%) judge that "Scotland's future is very important for the whole UK, and so should not be settled without the people of England and Wales being consulted in a referendum too". Fewer than one English voter in every three, just 29%, express contentment with the Scots determining their own course alone.

Conservative voters are particularly vehement in the believing that the whole UK deserves a say – some 75% of them say as much. Similarly high proportions of Tories back Cameron's belief that London should have a say in the ground rules of Scotland's referendum (76%), and insist that the UK is stronger together (73%).

The results come as the IPPR thinktank issues research which suggests that growing numbers of voters in England believe that their country gets a raw deal out of the union as currently arranged. The report finds that twice as many English voters as in 2007 now believe that Scottish devolution has left Britain being worse governed. It also charts an increasing tendency for the English to believe that the Scots get more than their share of public spending, although English opinion has not yet coalesced on any single response, such as barring Scottish MPs from voting on English laws at Westminster or establishing a separate English parliament. Tom Clark