I suppose this kind of idea is predicated on the notion that an independent UK would be able to get better terms than as part of the EU with these other nations, for these non European Imports.
On a like for like basis I find that extremely unlikely, given the bargaining power of a bloc like the EU. An independent UK could, of course decide to make other concessions like opening up the NHS to foreign bidders, or accepting lower standards than the EU (chlorinated chicken) but is that really the way we want to go?