Ah, fanks for explaining it all to me, Tuga, don't know where I'd be without you.
Steve, UK sovereign waters are just that, immaterial of who eats the fish that are caught in them. Some historic, pre-EEC conventions notwithstanding, for the EU to try to claim otherwise is directly comparable to the UK claiming a right to harvest 90% of the vineyards of Bordeaux on the arguably stronger account of the fact that we actually owned the bloody thing for a good few years a while back.
The CFP, and the CAP, were a stitch up that was completed by the EEC a week before the UK signed in. The former devasted the UK fishing industry within a few years - Grimsby had a fleet of 700 boats at its peak, it has 3 now - and wrought environmental carnage on the North Sea fisheries. The CAP ensured that the British taxpayer subsidised inefficient French farmers in perpetuity, whilst enriching the UK's own already wealthiest landowners.
Of course the pathetic rump of the UK fleet is incapable of efficiently and sustainably exploiting its own waters, but it is entirely reasonable that the UK controls them.