Considering that the European Union (EU) make 13-65% of UK laws (depends on how you look at it), it is important to examine the degree of democracy of EU institutions for their legitimacy.
Some may correctly point out that, for instance, European Parliament whose members were elected, has significant power (though may not be as comparably powerful as a national parliament at national level). However, as we learnt from the history, there are no shortage of examples of democracy only on paper.
Take China for example. Its National People’s Congress (NPC) in theory is the body with the greatest power in the country. It has the power to legislate, the power to oversee the operations of the government, and the power to elect the major officers of state, including the president. Its members are elected, though not directly. In much sense, the NPC seems very similar to the UK parliamentary system, at least on paper. Of course, except we know that it is a one-party state. The CPC is too strong in the NPC and there is no strong opposition party to hold it to account.
Obviously, the European Parliament is nothing like NPC. In fact, the problem is totally opposite: every party is a minority. For example, in 2014 European election in the UK, UKIP had taken 24 MEPs, making UKIP the largest among all UK political parties in this election. However, there were 751 MEPs in total in the European Parliament. This means a mere 3% representation, despite UK being the second largest economy in the EU, or around 17% of EU’s GDP; or having the 3rd larges population within the EU. With such a low representation, UKIP has no chance to effectively form/influence a governing body either on its own or through coalition (European Commissioners are appointed anyway). Now compare to the UK parliament which can form a government body by one or, less commonly two parties (coalition), when they have the majority of seats. While there were Scottish “minority” government, the ruling party still had large share of seats (e.g. the 3rd Scottish parliament). Everyone being a small minority means that there is no one who is accountable, and conversely no opposition to hold whoever to account. No wonder a shopkeeper had such a experience he shared in a TV debate: he asked every customer walking into his shop who their local MEP is, and not surprisingly no one had a clue.