The UK has maintained some of the strict regulations of the EU, particularly around food. If the EU and US get intro a trade war then either might attempt to monopolise British imports and exports by levying additional tariffs on things which originate in the other.

The US might attempt to push its industrial food industry onto us, as a price for continued trade and lower tariffs. The EU bloc all have to agree to trade in unison and might punish the U.K. for breaking away from the EU and seeking favourable terms elsewhere. I can see it getting messy.