At last, real hope in the eurozone. Its leaders finally set out a plan last week to solve the debt crisis. We need to see the detail but – for now – the markets approve and eurozone governments have bought themselves time.

Little was said about fiscal integration but that is clearly where the eurozone is headed. It is the only way to support continued monetary union and so the European landscape is about to change. European integration has always evolved in fits and starts, driven by crises and upheaval. Now it's happening again and the question is: how do we in the UK respond?

So far the debate has been dominated by two extremes. On the one hand, there are some who see an opportunity for a more centralised EU, built around a tighter, quasi-federalist core. On the other are those who imagine a chance for the UK to draw away from the union. They relish the prospect of a unilateral raid on Brussels' powers. The irony is that both options require treaty change: Europhiles and Europhobes are clamouring for the same thing.

As always, neither extreme of the argument is right. Both would have the UK give up our place at the European top table, sacrificing the influence essential to our prosperity. It is only by having a loud voice in a united Europe that we can promote the open economy that will deliver growth. Being shoved to the margins, or retreating there voluntarily, would be economic suicide: a surefire way to hurt British businesses and lose jobs. It would also leave us alone in the world at a time of great uncertainty. Eurosceptics tend to gaze longingly across the Atlantic, but the Americans are interested in us, in large part, because of our sway with our neighbours. We stand tall in Washington because we stand tall in Brussels, Paris and Berlin.

So this government will play our hand shrewdly, advancing our national interests in three key ways.

First, we won't run headfirst towards treaty change. The Germans are interested in very specific amendments to ensure that the budgetary rules for eurozone members are strict and adhered to. There is sense in that. But, having worked in the EU for years, my concern is that tampering with the EU's founding texts is opening a Pandora's box, leaving us paralysed by ideological battles, institutional navel gazing and special demands from every member state. These are dangerous distractions when our urgent priorities are restoring stability and jumpstarting growth. We understand the need for stronger fiscal discipline and oversight in the eurozone, but we must see if these objectives can be met by other means.

Second, the UK is forging alliances on both sides of the eurozone border. The government has worked hard to build up relationships across the EU. I've heard the case made that, should the eurozone become a club within a club, our natural place is as leader of the "outs" (the 10 states that have not joined the euro). But to limit our ambition like this would be an extraordinary own goal. Why would we seek to head up a smaller club with a fast diminishing membership? Many of our fellow "outs" eventually want to become "ins".

More important, we spent years fighting to bring down the walls that divided Europe – it would be damaging to let new ones spring up now. Liberals believe in integration because we understand that our nations are stronger together than we are apart. From the economy, to climate change, to defence and crime, co-operation between European countries has delivered untold benefits for every single person in the UK. Fracturing the EU would undermine those achievements. It should be avoided at all costs.

So two rival clubs is not an option. Clearly the "outs" share an affinity, but there are plenty of "ins" who are economically liberal and want the UK to take a lead. Some will also be anxious about being railroaded by powerful states within the Eurozone. I recently brought together trade ministers from 14 European member states – seven "ins" and seven "outs", as it happens – to join forces on a pro-growth, pro-jobs agenda. Such alliances will take on new significance now.

Third, the UK will push with all our might to deepen the single market – the world's largest borderless marketplace, made up of 500 million consumers. Economic openness is the glue that binds the EU together and it is the solution to the crisis of European competitiveness that long predates the current strife. Europe's populations are ageing, our productivity is low, and the world's powerhouses – India, China, Brazil – are racing ahead.

Breaking down the remaining barriers to trade is the single best way to get ourselves back in the game. By properly liberalising services and creating a digital single market we could add £700bn to the EU economy. That's the equivalent of making every household £3,500 better off each year. But these reforms need leadership, and the UK is well placed to provide it. The single market was, after all, a British invention, designed by Lord Cockfield, a British EU commissioner, and pushed through by the then Conservative government.

There is a growing majority of like-minded members who will support us, but we need to engage decisively and constructively. That is how you win the argument in Europe. Recent UK successes – for example on cutting red tape and moving towards better patenting rules – remind us of the benefits when we do.

Change in Europe presents opportunities, not just threats. The coalition will be strategic and long-sighted and we will not give up the influence that benefits the British people. Nor will we sit on our hands and allow others to take it from us. We will strain every sinew to promote British interests, and it is in an open, united and liberal Europe that those interests are best served.

Nick Clegg is leader of the Liberal Democrats and deputy prime minister