The rise of euroscepticism is not just a British phenomenon.

Across the continent, frustration with mainstream politics and the bleak economic outlook have fuelled the rise of anti-establishment and eurosceptic parties. For most people, this growing anti-EU sentiment does not stem from hostility towards the idea of European cooperation. The issue is that “Brussels” has come to be perceived as remote and unaccountable.

This malaise is symptomatic of a wider disillusionment with those in power and their failure to get to grips with the economy. Trust in the EU may have fallen in recent years, but trust in national governments remains even lower. Whether it is UKIP in Britain, the Front National in France or Beppe Grillo's Five Star Movement in Italy, eurosceptic parties have capitalised on the public's growing distrust of the political class. These parties invariably fail to provide a credible alternative plan. However, they thrive on the perception that national politicians and the EU institutions are out of touch with the concerns of ordinary people.

Download the new Independent Premium app Sharing the full story, not just the headlines

That is why, if David Cameron is to deliver an outcome acceptable to the British people, he must focus on reforming the EU as a whole to make it more growth-focused, transparent and relevant to its citizens. Other European leaders have stressed their desire for the UK to remain part of the EU, but also that they are not interested in cutting a special deal for the UK alone. They rightly stress that the single market relies on a common set of rules, applied and enforced equally by everyone. At the same time, many on the continent recognise that there is growing need for major changes. Rather than engaging in a fruitless attempt to repatriate powers back to the UK, Cameron should build alliances and work towards EU-wide reform.

The EU is not a state with a fixed constitution. It is a constantly changing organisation that must adapt to the challenges faced by its member states if it is to remain of added value. In the 1950s, it was focused on promoting post-war reconciliation and feeding Europe's population. The emphasis then moved to promoting free trade with the creation of the single market, driven by Margaret Thatcher. More recently, the end of the Cold War in the 1990s precipitated the spreading of democracy and prosperity across the continent through the process of EU enlargement.

The big challenges now faced by European countries: the debt crisis, declining competitiveness, tax evasion, climate change, terrorism and organised crime, require new solutions. In a globalised world, the ability of individual countries to manage powerful social, environmental and economic changes from within their own borders has been significantly reduced. We must work together in order to address common problems, promote shared interests, and maintain control over the forces of globalisation. The inescapable truth is that countries such as Britain no longer carry the same weight on their own today as they did in the past. Europe is about regaining sovereignty, not losing it.

This does not mean centralising all powers in Brussels or creating a European super-state. Indeed, I am of the view that EU institutions should spend more time developing solutions to Europe's debt crisis and less on regulating olive oil jars in restaurants. But in the areas where it adds real value, the EU must be empowered to act more effectively. In addition, national ministers have to take responsibility for their decisions in the EU Council instead of obscuring them and using Brussels as a scapegoat. Finally, we should look at how to improve democratic oversight and involve national parliaments more in scrutinising EU decisions.

A fully engaged and committed Britain would have much to offer in this process of reform. Britain's liberal instincts and diplomatic and technical expertise could help make the EU more outward-looking, competitive and less bureaucratic. Last week's radical overhaul of the Common Fisheries Policy, which will prevent overfishing, end wasteful fish discards and increase regional management of fisheries, is just one example of what can be achieved when Britain plays a full and constructive role. But to promote your own vision of what a reformed EU should look like, you need to have a seat at the table.

Some argue that upcoming financial integration in the eurozone will mean that Britain will be left sidelined in a future EU. But this is by no means a foregone conclusion. On many trade and economic issues, countries such as Germany, Finland and the Netherlands are far closer to the UK than they are to France, Italy and Spain. This is unlikely to change. In any case, Britain is not alone; nine other EU countries are not eurozone members. Together with like-minded countries, Britain can continue to play a leading role in steering the EU along a more open and liberal path.

In the past, Britain has never shied away from promoting its interests in Europe. It has always stood and fought for its interests and principles, profoundly shaping the history of our continent. If Britain were to turn its back now, it would risk the emergence of a different kind of EU, less concerned with British interests but also less liberal, weaker and with a less global perspective. This would be a grave mistake, both for the British people and Europe as a whole. Rather than retreating to the periphery, Britain should take the lead in building an EU that is efficient, accountable and fit for the 21st century.

Guy Verhofstadt was Prime Minister of Belgium from 1999 to 2008. He has been an MEP since 2009 and is Leader of the Alliance of Liberals and Democrats in Europe . On Monday night he speaks in a debate in the European Parliament on the future of the EU.

For Martin Callanan's view, click here