Fact Check - Is 80% of UK fish given away to the rest of Europe?

As a result of membership of the Common Fisheries Policy, we are now allowed to catch less than 20% of the fish that swim in British waters. The other 80% we have given away to the rest of Europe. Nigel Farage, UKIP leader, on the campaign trail 
When fact checking this statement, it is first of all worth pointing out that if the UK was allowed to catch 20% of the fish that swim in British waters and the EU took the rest, then there would be no fish left in the sea. In attempting to check the facts behind this assertion, one must assume, therefore, that Nigel Farage is referring to the allocations of fishing quotas which are determined by the EU’s Common Fisheries Policy (CFP).