From the European Environment Agency (an agency of the EU),
Combined EEZ of >15 million km2, the largest marine domain in the world
[Overseas entities] also contribute to a significant extension of the European Exclusive Economic Zone (EEZ), 60% of which is adjacent to the EU overseas entities making it the world’s largest and most diverse marine EEZ.
Thus, the non-overseas EU EEZ is approximately 6,000,000 km2.
From the Commonwealth Parliamentary Association, the UK's exclusive economic zone (EEZ) is 6,805,586 sq km. Thus, the UK's waters are, at best, 45.4% of the EU's. This value includes the British Overseas Territories, and isn't just the mainland UK (thanks @Robert Tausig and @Fizz for pointing this out).
The UK (mainland)'s EEZ is, according to Sea Around Us, 756,639 km2. This is 12.6% of the EU's total EEZ.
Regarding the Total Allowable Catch, The Conversation says
In 2015, the CFP allocated the United Kingdom a total of 612,612 tonnes of quota from more than 100 different fish and shellfish stocks. The total EU quota for these stocks was 2,069,202 tonnes, so the UK was allocated 30% of these fish (and shellfish) quotas.
As such, the UK was allocated 29.6% of the total allowable catch in 2015.
At present, the UK provides 50 per cent of the EU’s waters but receives only a 25 per cent share of the Total Allowable Catch.
The UK provides 12.6 percent of the EU's waters and received greater than 25 percent of the total allowable catch (in 2015). The claim is "flat out wrong". (thanks @Robert Tausig)
Note (per Fizz):
The total allowable catch is, according to Full Fact, set
based largely on how much [member states] fished in those areas in the 1970s, before the Common Fisheries Policy came into effect.
Thus, water area is not considered a principal factor in assigning fishing quotas. The fishing quotas are not assigned by "international law", but by the EU itself.
From the Scottish Fishermen's Federation, between 2011 and 2015:
Non-UK European Union fishing boats landed about 700,000 tonnes of fish and shellfish, worth almost £530 million, from the UK EEZ each year on average.
UK fishing boats landed 92,000 tonnes of fish and shellfish, worth about £110 million, from other areas of the EU EEZ each year on average.
Note: The total allowable catch for 2019 can be calculated by adding all the numbers here, here, here, and here for 1) the UK and 2) all countries. I have not done this yet (it's a lot of numbers).