The former Liberal Democrat leader Nick Clegg knows what it's like to lose an election and to lose it badly, but he displayed his usual optimism (some might call it denial) when he talked to his party's conference in Bournemouth. The result of the General Election hurt, he said, but there was now a Liberal-sized chasm in British politics waiting to be filled. His real concern, he said, was not for the survival of his party but for the survival of the UK after the EU referendum. "If we vote to leave the EU," he said, "I have no doubt that the SNP will gleefully grab the opportunity to persuade the people of Scotland to leave the UK as well."

Mr Clegg's concern is well placed. Nicola Sturgeon has repeatedly said a second independence referendum would be unstoppable if a majority of Scots voted to remain in the EU but were forced to leave because of votes in the rest of the UK. Constitutionally, this makes no sense (the UK is the EU member state and it is the UK as a whole that will decide its future) but that is unlikely to stop the SNP using an out vote in the EU referendum to further its cause and push for another referendum in Scotland. The real and present risk is that the end of Britain's union with the EU would also lead to the end of Scotland's union with the rest of the UK.

Where Ms Sturgeon and Mr Clegg agree is that a positive case must be made for staying in the EU and it must be made soon. What was remarkable about the Scottish referendum was the profound engagement of almost every Scot and a highly informed level of debate. Mr Clegg fears the EU referendum will fail to reach the same standard and that much of the debate will be ill-informed and rely chiefly on some of the old clichés. This places an obligation on supporters of the EU to present the strong, realistic, positive reasons for staying.

The first of them Mr Clegg alluded to in his speech. What kind of country do we want to be in a globalised world, he asked. Do we want to live in our own backyard, isolated from our nearest neighbours? They are fair questions and point to one of the most convincing reasons to stay in the EU: in an uncertain world, it makes sense to be part of a larger family of nations. Even in Greece, where membership of the EU can seem like a recipe for more hardship, the people have again voted for Syriza and by extension the tough conditions for their country's third international bailout; they appear to have judged that it is because better to stay united and work it out together.

The business case for staying in Europe is also convincing – EU membership is vital for Scottish jobs and leaving would do tremendous damage to the domestic trade that Scotland does with the EU. It is a point that Ruth Davidson, the Scottish Conservative leader, will make in a speech in Brussels. Her priority is Scottish jobs, she says, and the advantages of EU membership clearly outweigh any disadvantages in helping employers grow and expand.

Ms Davidson also addresses an important point which Mr Clegg did not discuss in his speech: reform of the EU. The Tory leader believes more autonomy should be given to member states, but the reforms need to go further. The EU needs to be more democratic and accountable, it also needs to be more responsive to its member states, and it absolutely needs to cut costs and bureaucracy.

It is still the most likely scenario that these arguments will be convincing in the end and that the whole of the UK will vote to stay in the EU. But with a Prime Minister seeking to appease his Eurosceptic right and a First Minister looking for the right circumstances to call for a second referendum, the stakes are as high as Mr Clegg says they are. Not just one, but two unions hang in the balance.