European waters are split up and administered by the countries which border them. Therefore a Spanish trawler (for example) wanting to fish in UK administered waters has to have a UK quota - obtained from the UK government (or organs of). The other method is to purchase a quota from a UK fisherman who already has one - many foreign fishermen have done this and there are some very well off UK fishermen (ex and current) as a result.
The reasons quotas exist in the first place is to ensure fish stocks are conserved, and came into effect due to the near collapse of European fishing grounds due to near-calamitous over-fishing in the decades upto the 1970s. Quite simply fishermen cannot be trusted to fish responsibly, because the more they fish the more they earn and UK fishermen were some of the worst offenders of the lot. Accordingly British fishing grounds suffered more than most.
Any fishermen out there who think our exit from the EU will mean the end to quotas and a free for all (for them alone) in UK waters are delusional. It will not happen because the government of the day cannot not listen to the scientists and ecological advice. Yet bizarrely that's what they all think will happen!