Tensions have already risen on both sides of the Channel following David Cameron's recent rejection of any new treaty which did not give the UK reasonable safeguards against damaging new single market and financial services regulation.
These tensions can only rise further. Three years from now, a new voting system will mean the eurozone countries can caucus to outvote the UK and other non-eurozone countries in all areas of legislation governed by qualified majority voting.
That may begin to look more like subjugation than isolation.
For negotiating purposes it must make sense to know how the UK could walk away from the table. But the strange thing is that neither of the most widely canvassed ways for the UK to leave the European Union (EU) would actually work.
Some say we could just leave the EU without any new trade agreement and rely on the World Trade Organisation (WTO) agreements to protect us.
But the immediate consequence of such unilateral withdrawal would be that UK-based car manufacturers would immediately face the same 10pc tariff on their exports to the EU as car manufacturers based in the US or Japan.
Most UK chemical exports would face EU tariffs over 5pc.
Others say we could negotiate a new free-trade agreement with the EU like Switzerland or Norway. But a free-trade agreement only provides for duty-free trade in products manufactured or partly manufactured in the area it covers.
The EU would not want cars manufactured cheaply in China imported duty-free via Norway to avoid the 10pc tariff rate with which it protects EU-based car manufacturers.
Under an EU-UK free-trade agreement all UK merchandise exports that would otherwise be subject to EU tariffs would have to be tested for compliance with what are known as "rules of origin". These are often highly complex.
Imagine how manufacturers in Yorkshire and Lancashire would react if they were told that in future goods could only be trucked across the Pennines duty-free if they complied with the relevant rules of origin.
British and Continental manufacturers would surely react similarly to the introduction of rules of origin testing on goods they were shipping across the Channel.
There is a basic confusion here. The free movement of goods which the single market provides for, without let or hindrance, is far superior to rules of origin-based duty-free trade under a free-trade agreement.
So if the UK left the EU it would be vital to retain free movement of goods, in the best interests of both ourselves and our European trading partners.
That would mean agreeing to stay in customs union with the EU and retaining EU tariff rates on most of our imports from the rest of the world. But we would be doing this as an independent country, on an inter-governmental basis in place of the present supranational one.
Having to retain EU tariff rates would not be so bad. Average EU tariffs on manufactured goods are only 2.7pc. Few would argue for lowering UK car tariffs below the current EU level of 10pc unless other countries did the same.
We would continue to be stuck with relatively high EU tariffs for some food imports. But that would be a small price to pay for continued free movement of goods.
As the second-largest net contributor to the EU budget, the UK would surely have the whip hand in negotiation. Logistically, it would be relatively easy to switch to an inter-governmental customs union agreement. Morally, we would have the great strength of being able to say we wanted to stay in Europe for trade, which was what the British people voted for in their 1975 referendum.
We could negotiate at least as good access to other EU services markets as we have at present. We would no longer need to contribute towards the excessive levels of trade-distorting agricultural subsidy other EU member states dish out under the Common Agricultural Policy.
A huge benefit would be that we could take back from Brussels control of supervision and regulation of the City. And there would be no possibility of a new Financial Transactions Tax being forced on us.
Granted, there would be a small downside in no longer being able to participate directly in the EU's Single Market rule-making process. But in truth there are few exclusively indigenous UK exporting industries which could be vulnerable to deliberately discriminatory regulation.
Lastly, there would be real attractions in continuing to work alongside the EU for future international trade liberalisation. The fact is that in three successive negotiating trade rounds since 1964 the EU has brought its average industrial tariff down from over 10pc to the current 2.7pc level.
The EU's recent free-trade agreement with South Korea is genuinely trade liberalising. And it is not the EU's fault the Doha round of WTO talks has stalled.
Most people in Britain want our EU membership to work. But if current trends continue the British government will need to consider much more radical options than it has to date.
Ronald Stewart-Brown is director of the Trade Policy Research Centre, which has recently established an office in Westminster.