Every year the International Council for the for the Exploration of the Sea and the European Union's Scientific, Technical and Economic Council for Fisheries make a suggestion of what the TAC should be for each stock. A stock of fish refers to a "particular species of fish caught in a particular geographic area". The European Commission drafts a proposal based on these suggestions. After this, fisheries ministers of the various EU countries meet in the Council to reach agreement on what the next year's TAC should be. While their decision supposedly takes the scientific advice into account, the ministers have the option to deviate from it and often do by simply increasing the TAC.
After the TAC is determined, this divided among the EU member states who further divide them among companies and individuals. While the TAC changes every year, each member's proportion of the TAC does not and remains constant. Under the EU proposal, if Britain and the EU do not agree on a TAC before the 24th of December each year, the Total Allowable Catch (TAC) recommended by the ICES would have to be adopted. This would effectively be ceding British sovereignty and control over British waters to Brussels. If Brussels does not agree with the TAC Britain wants to impose, the ICES recommendation has to be accepted. This gives Brussels a veto over any British decision regarding TAC. 
The EU wants quotas to be fixed, preferably at the current rate which is based on a reference period of 1973-1978 (known as the principle of 'relative stability'). This reference period actually disadvantages Britain since British fishers fished mostly around north Atlantic waters (rather than around the UK) which were closed after the UNCLOS was signed in 1982. Furthermore, even if quota numbers were different, it is in the British interest to negotiate quotas on a yearly basis. This is because it will allow quotas to be adjusted based on changing economic, diplomatic and ecological conditions. For these reasons I believe that these proposals should be rejected. 
If no agreement is reached, Britain and the EU will have full control over their respective EEZ's. This means that British fishers will have no right to fish in EU waters and EU vessels will have no right to fish in British waters. Britain has leverage on this issue since EU vessels catch more fish in British waters than British vessels catch in EU waters. However, Britain and the EU would have to cooperate to address the issue of fish stocks shared between both of them.
The British decision to join the EU (or what was then the EEC) was extremely detrimental to the British fishing industry. Boats had to be withdrawn till they were a fraction of the previous numbers. Coastal ports saw a huge decline since the industry they depended on shrank to a fraction of what it was originally. Jobs that relied on fishing declined and there was a rise in unemployment in what were once prosperous ports. This decline can be reversed, and these negotiations are an opportunity to work in that direction.
Europe needs the British market, refusing to a trade agreement with the UK if Britain refuses to accept EU demands on fisheries will just be shooting itself in the foot. For example in 2015, 14% of Irish exports and 7.4% of German exports went to the UK.  It is not in the EU's interest to lose free access to the British market and this should be kept in mind. For this reason, Britain is negotiating from a position of strength.
Many argue that the UK will have nowhere to export fish to, if an agreement is not reached with the EU. If we were to listen to the European Commission, we would believe that if talks broke down and the EU imposed tariffs, Britain would be unable to sell fish to the EU market. Firstly, food demand is non-elastic which means that the demand for fish sand other marine products will not be affected by a tariff induced price increase. The losers in this situation will be EU consumers who will just pay higher prices.  Even if we were to accept the European Commission's theory and assume that tariffs will have some impact, there will still be an increase in British fish catches and exports. Secondly, the EU is not the only consumer of fish. Even if the European consumer market for British fish was lost, this could be made up by exporting to non-EU markets such as the USA.
The US imports the vast majority of its fish, there is no reason why British exports cannot be increased. In Fact, the US is already the largest importer of UK Salmon, making up 32% of British salmon exports in 2012, which is equal to 32,105 tonnes. Currently, the US imports lots of Chinese fish, however, with the increasing belligerence and aggressiveness of China, this is likely to change. The UK fishing industry could be a beneficiary from such a development. If not the US, there are countless other countries outside the EU where British fish can be exported to. Currently, 40% of British fish are caught by EU members. Due to Brexit, the UK government can now decide what size quotas will be given to other countries, assuming it does permit these nations to catch at least some fish in British waters. Regardless, of what approach the government takes, it should ensure that the amount and proportion available to British fishers is much higher than before (adjusting for resource preservation). This will allow British consumers to enjoy fish at a lower price and will also allow fishers to export part of the increased supply to other countries.