Prime Minister Cameron gives a speech following the election result. (Flickr/Number 10.)

So the next five years in Britain look set to become a tale of two unions: the centuries old union between Scotland and the rest of the UK, and Britain's relationship with Europe. And although polling day produced an unexpectedly clear result, rarely has an election brought with it so much national uncertainty.

On a night when the tectonic plates of British politics not only shifted but completely changed shape, the success of the Scottish National Party provided perhaps the largest drama. In the 1950 election, it received just 0.5% of the vote. Last Thursday, it attracted 50%, winning 56 out of 59 seats. So does this near monopoly on Scotland's seats at Westminster mean that independence is now inevitable, and that the supposedly 'once-in-a-generation' question posed in a referendum only last year will soon be revisited?

Here it is worth remembering that the SNP leader Nicola Sturgeon, the undoubted star of the campaign, ran against Westminster-imposed austerity rather than Westminster-imposed rule, although many of her supporters doubtless conflated the two. She did not set out to make the 2015 general election a re-run of the 2014 referendum. Nor is she demanding a new referendum in the near term. What's more, half the Scottish electorate voted for parties other than the SNP.

But with the politics of Scotland so divergent from the politics of the rest of the country – in Northern Ireland, the pro-union DUP ended up with the most seats – the sense of grievance and separation may well grow, and with it more urgent demands for independence.

For all the party's newfound strength at Westminster, the SNP could have ended up in a far stronger position in the event of a hung parliament. Had Labour required its tacit support to form government, Nicola Sturgeon might have ended up as Britain's second most powerful politician. Now that the SNP is the third-largest party in the House of Commons, it might become harder to prosecute the argument that Westminster is alienated from Scotland.

In the end, the future of the union might well turn on the new Conservative government's response to the Scottish question. Senior Tories such as London Mayor Boris Johnson have already raised the possibility of a new constitutional arrangement: some form of federalism or 'devo max', which would grant full fiscal autonomy.

But to those who think that Scottish independence is now all but inevitable, the example of Quebec might be instructive.

So much power flowed from Ottawa to Quebec City after two failed referenda, in 1980 and 1995, that devolution quelled much of the ardour for independence. French Canadians experienced many of the benefits of quasi-independence, such as determining their own immigration rules and Francophone education policies, without suffering the economic pain. Now, there is no great appetite for a third referendum, especially among the young.

Along with the Scottish question, the English question looms large. The huge number of Westminster seats now occupied by Scottish nationalists makes it even more apposite. Many English voters are already disgruntled that Scotland receives a disproportionate share of government spending. In the final days of the election, the fear that Nicola Sturgeon might unduly influence Ed Miliband became a vote-winner for the Tories. The English are also restless.

Over the next two years, however, British politics will be dominated by the European question: the possible withdrawal from the EU or, to use the shorthand, 'Brexit'. David Cameron has promised an in-out referendum on Britain's continued membership of the European Union by the end of 2017.

Personally, he wants Britain to remain part of a reformed EU. He rejects of the notion that Europe should be 'an ever closer union'. But Germany and France, the countries that have driven closer integration, are opposed to the Cameron agenda. For all that, Angela Merkel and Francois Hollande might be willing to grant concessions on voting rights and immigration rules that would enable Cameron to argue in the run-up to a referendum that his demands for reform have been partially met.

Jean-Claude Juncker, the EU's new chief executive, has already offered talks on reforms aimed at cutting red tape. But the EU has also made it clear it will not agree to major treaty changes such as ending the free flow of immigrants from poorer countries to the rich, which has caused such resentment in Britain and fueled the rise of UKIP.

Maybe now that Cameron has a majority of his own, he will be viewed in Europe as a more forceful leader, strengthening his bargaining position. But that cuts both ways. EU leaders will be hoping that because Cameron achieved a clear-cut victory, he will be able to sell more modest reforms in a referendum.

Brussels would have noticed that the election showed political nationalism to be a strong force not only in Scotland but in England as well. That usually translates into anti-EU sentiment. Though UKIP secured only one seat in parliament, it gained 12.6% of the vote. Its previous high was 3.1% in 2010. The Conservative Party also has a vocal Eurosceptic wing. Its most powerful figure is Philip Hammond, who will continue as Foreign Secretary.

Just as the election campaign was inward-looking, the next five years may well see the same myopia. The two great questions of sovereignty and independence could easily suck up much of the national bandwidth. Besides, with deeper cuts to the defence budget expected, reducing it to below the NATO guideline of 2% of GDP, military interventionism will become harder.

Those defence cuts could put further pressure on the special relationship with Washington, that pillar of British foreign policy. So, too, the commercial thrust of David Cameron's foreign policy, in which Britain has sought closer ties with China. The Obama Administration, angered by the UK's decision to join the Asian Infrastructure Investment Bank, has already bemoaned what one senior Administration described as ' a trend toward constant accommodation' with China. Those are the two obvious stress points in the relationship.

One hates to quote Dean Acheson's famous putdown that Britain lost an empire and failed to find a role, but it has echoed down the years primarily because of the UK's uneasy relationship with the rest of Europe. Now it also faces a more existential dilemma: does the United Kingdom still want to be the United Kingdom?