That's only half the story though :). The elephant in the room that the Brexit campaign fail to adress is that the WTO rules have tarriffs and quotas. Once you've sold your quota you are either prevented from selling more or the tarrifs are prohibitively high and you effectively sell at a loss and there is plenty of extra capacity in Europe to fill the void of British exports.
Meanwhile German, French and EU exporters are going to do what when they run a massive trade deficit with us, cheer on the EU as the UK imposes reciprocal tariffs on EU exports. The EU today is weak, the euro debt crisis is still with it and the migrant crisis threatens to overwhelm it, even Schengen is at best in suspension, fences and closed borders are going up all over the EU. The last thing the EU needs is a trade war with the UK and the EU knows it, only Remainers desperate to keep us in a failed declining EU won't admit it.