If Britain enters the Euro, one of the requirements is that control over monetary policy (the control of the money supply to the British economy) must be handed over to the ECB (European Central Bank.) The purpose of monetary policy in modern economics is to speed or slow consumer spending in order to balance competing factors of economic growth and inflation. The argument on this point therefore rests on the case that the economies of the EU states are similar (or converged) enough to have a "one size fits all policy."
Example: The best practical example that emphasizes this is Southern Ireland (which was grapping with double figure inflation) and Germany (which had major unemployment problems at the same time.) One state needs interest rates to move one way, the other needs them to move the other, therefore this is unworkable.

When countries begin to decline economically and unemployment rises there are normally patterns that go along with this, such as the currency of that country becoming cheaper because of declining trade. This means a price signal is sent to the free market, and investors will seek to put money in as it highlights a weak area that can be revitalised, and money can be made from both the currency movements and the growth of industry. If we have the Euro, this patterns are less obvious, meaning investment is either likely to go outside the Euro Zone where higher returns can be made, or simply not be noticed. In either case, this will hinder economic recovery and prolong unemployment in the depressed area.

The argument states that one way we define ourselves as a state is through our currency. In joining the Euro we lose that sense of "Britain" and see a cultural loss in a state which is already struggling with an identity problem.