It is a pity that Ed Miliband timed his announcement ruling out a formal coalition with the SNP on the day of Nicola Sturgeon's latest speech to the metropolitan thinking classes in London.

Perhaps Labour didn't want too many of their own supporters hearing it in case they found themselves agreeing.

The First Minister's speech to the London School of Economics, like her last one at University College London last month was thoughtful rather than polemical. Quoting the Labour thinker, Beatrice Webb, she explored the options for a broad "progressive alliance" with Labour and others.

It certainly didn't merit the Daily Telegraph headline: "SNP: we have right to dictate to all of Britain". The Ms Sturgeon insisted that the SNP wanted to work with parties towards parliamentary reform, for example in translating Holyrood's budgetary cycle to the UK.

The Scottish Government has to publish a detailed draft budget four months before the Budget bill is placed before Parliament. This means John Swinney can't play the UK Chancellor's game of pulling rabbits out of the hat at the last minute to wrong-foot the Opposition.

These usually end up wrong footing the Chancellor, as the omni-shambles budget of 2012 demonstrated. It is a daft way to run a whelk stall. The First Minister also called for the UK budget to be subject to an equality assessment as it is in Scotland, from the Equality Budget Advisory Group. This is not a bad idea.

Ms Sturgeon then went on to make the case for minority government - quite astonishing for a First Minister who is sitting on an overall majority in Holyrood. "When we were in minority we could only win votes by winning arguments," she conceded and continued: "Sometimes we had to compromise. That process can and often did lead to better budgets."

In other words, the old winner-takes-all approach mitigates against good government. Well said. No doubt, some opposition MSPs will quote this back to her during the 2016 Holyrood election campaign: "But Ms Sturgeon, didn't you say that an SNP majority was a bad thing?"

Of course, her main purpose yesterday was to lay out her vision of how the SNP could support a minority Labour government in Westminster without seeking seats around the cabinet. Any such pact would be based on two principles: First, that the SNP would always vote to keep the Conservatives out of power and, secondly, that any support would be on an issue-by-issue basis.

So, the SNP would support initiatives such as extending child care and increasing the minimum wage, but not foreign wars or welfare cuts. When it came to confidence motions in the House and on the Government's Budget, the SNP would vote in whichever way prevented the Conservatives from getting back into power.

This is actually what Mr Miliband was hinting at when he formally ruled out a coalition (which neither of them actually wanted) while not ruling out a looser deal. He is clearly thinking what the First Minister is thinking, though I don't know if Jim Murphy is.

But there are problems. To keep the Tories out, the SNP would probably have to vote with a Labour government's Budget, or at least abstain on it, depending on the arithmetic. Critics will say that this in itself means the SNP would be tacitly supporting both spending on Trident and austerity cuts in public services.

But I suspect that this could be finessed. Moreover, as the First Minister also said yesterday, it is surely time to question the renewal of Trident, which she said would eat up 10 per cent of the UK defence budget.

At a time when there is a crisis in Britain's conventional defence capability, aircraft, boats and personnel carriers could prove of greater use than an anachronistic nuclear system designed to destroy cities.

The more I think about it, the more I suspect Labour just didn't want this speech getting too much of an airing. It's in interests of both the Tories and Labour to suggest that the SNP are militant, blue-painted chauvinists whose only interest is in breaking up Britain and demanding money with menaces.

But Ms Sturgeon said the SNP accept the verdict of the September referendum. They're looking to play as much of a constructive role in government as possible. That's surely good politics in Westminster as in Scotland.