The question: Rosemary asks BBC Radio 4's PM programme "Would the UK have its fishing waters returned to the pre-EU status if we vote to leave?"
Reality Check verdict: It depends on what kind of agreements the UK makes with the EU and whether it would allow foreign vessels to access its Exclusive Economic Zone (EEZ).
Under the Common Fisheries Policy, European fishing fleets are given equal access to EU waters and fishing grounds up to 12 nautical miles from the coasts of EU member states.
The Common Fisheries Policy also aims to ensure that fishing and aquaculture across the EU are "environmentally, economically and socially sustainable".
A 2016 House of Commons Library paper suggests that were the UK to leave the EU, the resulting status of its fishing waters would depend on whether the UK would allow access by foreign vessels to its Exclusive Economic Zone (EEZ).
Outside the EU, an EEZ extends 200 nautical miles (370km) off a country's coastline, giving the state the authority to exploit and control the fish resources within this zone.
The House of Commons Library notes that if the UK allowed access to foreign vessels as part of the exit negotiations, it would have to "maintain a very close working relationship with the EU to enable the monitoring of landings and to co-ordinate on wider regulation in the sector".
"It would also have to agree some kind of mechanism for agreeing catch limits," it adds.
When Greenland voted to leave the then European Economic Community in 1982, much of the negotiations focused on fisheries agreements.
In the end, Greenland was given tariff-free access to the EEC market for fisheries products.
In return, it allowed continued European access to its waters.
On the other hand, the UK could decide to exclude foreign vessels and assume full responsibility for fisheries in its EEZ.
In that case, the House of Commons Library says, "there would be a number of implications for the UK and the management of fisheries in the area".