It really doesn't, countries managed trade just fine back in the day without the aid of gigantic empires, why people keep using this bullshit line I'll never know, you don't need a giant organisation to do the job of one transport and two people signing a piece of paper. People are deliberately trying to make the EU seem more necessary than it actually is and besides, it's showing that it is absolutely useless at organising itlsef and achieving it's goals so why bother?
The UK used to want a gigantic empire, that was the Commonwealth. The EU is probably the last chance for the UK if it wants to keep on having a voice on the world scene. No, frankly, who cares about little britain? If the UK leaves the EU, it will be much more difficult for british exporters to sell their goods in Europe, this is the only thing which should matter. The pound would sink, the Spanish would invade Gibraltar, of course the british would rule everything in their smallish rainy islands, but there would not be much left to rule. Note that businesses want to stay in EU.