The two obvious conclusions that almost everyone has drawn from the General Election are that Scotland has become much more nationalist and that England remains profoundly conservative.

As with so many obvious conclusions, both those assumptions are wrong. In politics, in any case, there are no conclusions: there's always someone with a bright idea for making things better, more's the pity. Usually, this is what the Germans call Verschlimmbesserung - an improvement that makes matters worse.

They might call those electoral conclusions Fingerspitzengefühl, a feeling in your fingertips, were it not that it usually carries the suggestion that the intuition is correct. Nobody could argue that the Scottish National Party's having taken all but three seats was anything but a resounding triumph. And it's natural to think it suggests a huge appetite for independence. Similarly, the fact that, despite the polls, the Conservatives gained an overall majority, might seem to indicate that there are large numbers of what some commentators have called "shy Tories".

But according to the Scottish Social Attitudes survey, the numbers of those who describe themselves either as Scottish but not British, or more Scottish than British, has been declining substantially since devolution was introduced. In 2000, that was 68 per cent of the population; last year it was 49 per cent. That was in the midst of the referendum in which 55 per cent voted No.

Nicola Sturgeon has been candid in admitting that a vote for the SNP is not necessarily a vote for independence and time and again insisted, whether you believe her or not, that a second referendum was not on the cards in the foreseeable future.

Meanwhile, the section of the electorate that voted for the Conservatives in England is the same as that which provided majorities for Tony Blair: the centre ground of swing voters. Conservative gains were at the expense of Liberal Democrat and Labour MPs. That destroys the notion that there was some huge right-wing English hinterland without which the Tories could not win.

They did win outright, and without Ukip's 12.6 per cent of the vote, which indicates that those who backed the Conservative this time are not "shy" diehard Tories, but ordinary voters who believed two things: that David Cameron was better than Ed Miliband, and that the Tories would govern better than Labour.

All the same, the current distribution of seats at Westminster opens up the potential for further division. Mr Cameron's talking-up of the dangers of a Labour-SNP coalition may have been a successful election tactic, but many will have seen it as an irresponsibly dangerous ploy from a Unionist party.

Be that as it may, it obviously wasn't the primary cause of the SNP's victory, and there would have been serious challenges to the Union no matter which party had prevailed in the rest of the UK.

So far, the announcements from the Prime Minister give every reason to suggest that he is serious about delivering the levels of devolution all the Unionist parties agreed on before the referendum. The tricky balancing act required of him, however, will be to reassure the electorate in the rest of the UK that other parts of the country are not being short-changed because of the Scots. The Union must change, and change radically, if it is to survive.

Hence George Osborne's speech yesterday, and the promise of further devolution not only for Scotland and Wales, but for the major cities of England. The model drawn up for Manchester looks like a useful template, offering local control of transport, planning and policing, but the trouble with the Cities' Devolution Bill, which will be presented in the Queen's Speech, is that many cities and regions show little enthusiasm for adopting the blueprint.

It is, in any case, harder to divide England into natural regions for devolved powers, even if they wanted them. Several have rejected the opportunity to create directly elected mayors (a precondition of devolution). And while the "Northern Powerhouse" project sounds like a long-overdue recognition that the degree to which the UK's power and wealth is concentrated in London and the south-east is unhealthy, in the Chancellor's words, for both our economy and our democracy, it is a far cry from being a fully worked-out model for federalisation.

The failure (at least so far) of anyone to devise a logical and practical resettlement of powers for the English, however, need not mean that some form of solution cannot be found. England has no shortage of constitutional oddities and illogicalities (the House of Lords is perhaps the outstanding example) that nonetheless, more or less, work.

No one thinks that the proposed solution for English Votes for English Laws is very tidy. It's reminiscent of the Scottish Grand Committee, which, in another example of constitutional untidiness, is still theoretically in existence, though it is now utterly redundant and hasn't met for more than a decade. But does that matter, as long as it satisfies English voters?

It's not only in the Union's, but Mr Cameron's, interests to ensure that the changes promised for Scotland are delivered. But it's also in the SNP's interest (at least, their short-to-medium term interest) to ensure that, while holding the Government's feet to the fire, they do not over-reach themselves.

The natural instinct of those convinced of the case for independence is, very naturally, to seek to find an opportunity to have another vote on the issue. But only at a point when they can be fairly sure they will win. The SNP's triumph may have been many things, all excellent for Nationalists, but it was no cast-iron guarantee of that.

It's not a question of the SNP extorting the best deal for Scotland - that's their mandate. But the Conservatives have a mandate too, and the majority to deliver their manifesto, including the further devolution of powers.

And while the Scottish electorate is certainly ill-disposed towards the Tories, that received wisdom is overstated. The party got 15 per cent of the vote - with potential supporters knowing they had no chance in almost every seat.

But ordinary Scots may not welcome contrived claims that they are being short-changed in order to provoke a row, or a rerun of the referendum. Similarly, it is impossible to maintain that further extensive devolution must occur, but that the Barnett formula must remain untouched, or be increased.

Next year's Holyrood elections and the following year's EU referendum will be obvious flashpoints. But the job of both the SNP and the Conservatives is to live up to what delivered victory for both parties, and to find an accommodation for their quite different manifesto commitments. That's going to take a degree of trust and goodwill, and not just from Westminster. Each party is equally at risk of alienating voters if it is seen to be ignoring its own, or the other's, mandate.