The main complaint of those who oppose the direction they believe the EU is headed, namely towards becoming a super-state, is that majority of the legislation made in Westminster these days is merely the transcribing of legislation from Brussels. "Brussels" is spoken about as if it is an entity completely separate from the UK, of which the UK is certainly not a part (Side note: at the post office one can buy three kinds of stamps: UK, Europe, international. Another reminder that the island sees Europe as something outside of the UK.) This view is partially based on fact, because something like 70% (I think) of legislation being passed in Westminster originates from the EU. But it is also partially misguided, since that the Council of Ministers has the final power to take decisions on the majority of EU legislation, and the UK has a seat at the table in the Council of Ministers. The image of Brussels being an anonymous legislation-making machine separate from EU member states themselves is a misunderstanding.
A second complaint is that the Eurocracy produces loads of unnecessary red tape and that the Eurocracy's administration consumes large amounts of resources. The former statement describes a two-sided coin. On the one hand, sharing governance horizontally between nation-states and vertically between different levels of supranational, national, regional, and local government creates an administrative nightmare, where certain pieces of the same policy must be approved by different levels of government and each level of government involves a variety of actors (e.g. Supra-national level = European Parliament, Council of Ministers, European Commission, committees, etc; National level = chief executive and cabinet, parliament, advisory committees, etc.) On the other hand, streamlining the EU's policy-making process would certainly mean leaving out some actors' ability to check and balance the decision-making power of other actors. Thus, some call it red tape, others might call it democracy in action.
As for the latter point, the consumption of resources towards EU administrative costs, this only constitutes 3,5 to 4,5 percent of the budget for the 2007-2013 financial perspective. This figure hardly compares to the 30 to 45 percent of government budgets that European state administrations typically consume. A final complaint is that aside from the Single Market, and particularly the free movement of people, there is no benefit for the UK to being in the EU.
This last point I would like to leave open for debate. To kick it off, I encourage you to watch a clever video: What has Europe ever done for us?
On the whole, I find that English criticism of the EU is based on grains of truth that only reveal the tip of the iceberg, but which have nonetheless become conventional arguments that perpetuate a misunderstanding of how the EU works and the UK's role within it.