So every shipment then needs to be checked to see if it competes with a UK producer?

If only .01% of the imports from a source country are problematic, 100% of them need to be checked, with all that implies.

One thing I expect to happen: supplies of illegal drugs will expand enormously. The customs people will be so snarled up looking for illegal catfood you'll be able to haul cocaine by the containerload undetected.