Just what is the UK’s problem with Europe?

It's the question markets are dismissing with a shrug at the moment – but it's going to get more pressing very soon. After more than four decades of (mostly) happy marriage, the U.K. is approaching an in-out vote on its membership of the 28-country European Union.

Thanks to the unexpected electoral victory by the Conservative Party, traditionally the most sceptical towards Europe, the referendum is fast becoming a reality.

The Queen's Speech on Wednesday is expected to contain an EU referendum bill, as the path towards a vote looks potentially shorter than anticipated, with some now talking of a referendum in 2016 rather than 2017.

Stock markets appear to be shrugging off the prospect of the U.K. leaving the EU (summed up in the term "Brexit). Recent tests of public opinion, such as the Scottish independence referendum and the election, suggest the British public likes the status quo. Opinion polls suggest around 39 percent would vote to quite the EU in a referendum.

Yet public opinion on this issue has proved volatile in the past, and U.K. pollsters notoriously failed to predict the outcome of the recent general election. A low turnout could give the No campaign, whose voters are likely to be more fervent, a boost.

Here, we take a look at some of the issues driving the debate over the U.K.'s future in Europe.

The U.K. is a net contributor to the EU – as are other large economies like Germany and France. The money is used across Europe to ensure a level playing field for the EU's poorer countries by being invested in for example, new roads or broadband. However, the bill is rising as the U.K.'s economy improves, with a net contribution of £11.3 billion ($17.4 billion) in 2013 , compared to £2.7 billion in 2008, according to official UK data.

One of the economic arguments often put forward for Brexit is that EU membership is hampering the U.K.'s trade ties outside the trading bloc.

EU membership would be replaced by "new economic commerce with the whole world", according to pro-Brexit lobby group Global Britain – but the extent of this commerce is uncertain, and markets, as the cliché goes, dislike uncertainty.

It is difficult to seriously argue that EU membership is a greater barrier to trading with China -- to mention one country where the U.K. government is devoting a lot of effort -- than the long-term decline in U.K. manufacturing. Proud euro zone member Germany exported 74.5 billion euros worth of goods to China last year, more than five times the value of U.K. exports to China.

Why wouldn't we want free trade with our largest market?" Lucy Thomas, campaign director at pro-EU lobby group Business for New Europe, told CNBC.

"We have so much more clout negotiating trade deals as part of that group rather than on our own."

Freedom of movement for labour is one of the key principles of the EU, and with more than 14 million citizens, from footballers to fruit pickers, living in an EU country which they weren't born in, it affects a lot of people. This ease of movement has been attacked in the U.K., which had an unexpectedly high level of migration from several old Soviet bloc states after they joined the EU. Some of the blue-collar workers who felt threatened by this new, cheap, source of labour subsequently turned towards Nigel Farage's U.K. Independence Party. Another key point of aggravation is the right of migrants to claim welfare benefits in the U.K. – which Cameron is trying to revoke.

One focal point for alleged European control over U.K. laws is the influence of the European Court of Human Rights, which in certain high-profile cases has made it harder to deport foreign-born criminals. If the U.K. moves away from the ECHR's influence, it would be in company with isolated Belarus as the only European countries not to comply with it.

As the euro zone's fiscal ties are tied tighter following the credit crisis, there are concerns that the EU members who held on to their own currencies, including the U.K., Denmark and Sweden, may not have enough influence over decision making.

In the event of a Brexit, those pro-EU membership argue, the U.K. won't be able to change EU policies – but will still have to deal with their consequences.

"It makes no sense to disengage from our major market where we would still face all the costs of compliance and enjoy none of the influence. We can achieve reform by being an active and leading member from within," Terry Scuoler, chief executive of U.K. manufacturer's association EEF, argued.

- By CNBC's Catherine Boyle