And I didn't answer the first part of your post @SerendipityJane. For a trade deal, all foodstuffs will have a tariff negotiated for each one with a preferential rate lower than the WTO rate.
The US doesn't export hormone beef or chlorinated chicken to the UK currently. UK customs authorities could stop these exports under their own powers by inspecting the certification that comes with each export on the origin of the goods.
In a trade deal, it is only those goods negotiated that get preferential rates. Each deal also provides for dispute resolution via arbitration independently.
The EU is the outlier here because it would like the UK to be subject to the European Court of Justice to resolve conflicts on food standards. The UK does not have to accept that, and it is very unusual to have a preferential trade agreement where the parties agree one party's domestic legal system will have that power.
This is why Farage et al get their arguments. The EU ask for a conspicuous WTO plus arrangement which they can affect by means of their own regulation. Now as a member of the EU you can trade this off as part of an overall deal which is good for a country. But piecemeal it is probably a bad deal if you are outside, as the UK now is.