We need a European policy because fish wander. There is no point in protecting the adults in British waters if the piscine children and teenagers are being massacred in, say, Dutch waters. Purely national solutions do not work. The CFP is based on supposedly scientific limits on the number of fish that can be caught. The permitted annual catch is divided into quotas for national fleets. The size of those fleets is not restricted. In theory, at least, the least productive boats in a national fleet should be driven out of business and the industry should find its equilibrium, with just enough boats catching just enough fish.
However, in practice, that does not happen. Governments pander to fishermen and inflate the catch levels recommended by the scientists. The policing of quotas and net sizes has been inadequate. British fishermen were rightly incensed by the recent European Court decision allowing member states to poach each other's quotas by registering fishing vessels in other countries ("quota-hopping"). This makes sense under single market rules, but it blows the CFP apart.
As a result of loopholes such as this, Europe has too many boats chasing too few fish. A more effective solution would be to impose a much stricter system of licensing on boats to restrict the size of fleets. This could be combined with a market to auction and then trade the licenses. This mixture of EU quota setting and market trading for licenses would be much more effective in preserving fish stocks and managing a more orderly contraction of the industry, thereby helping to limit the damage to traditional fishing communities.