Governments don't trade goods and services. Companies and individuals do and governments get – more or less, according to how economically idiotic they are – in the way. Most "trade deals" are to remove tariffs created by governments in the first place. The other kind of "trade deal" is the symbolic nonsense flourished at international summits so that the politicians can pretend that they have "done something" about job creation. "Trade deals" only make trade easier when the governments concerned made it harder in the first place.
All governments really trade is insults, ordnance and corrupt advantages for politicians.
All of this idiotic talk about being on the inside when making trade "rules" is therefore so much political blather. The main "rule" that matters is the law of supply and demand. I will buy Italian cars if they suit my needs better than German or British cars at the price point I can afford. I have bought all three kinds – and even a disastrous French one – in my time, according to my perceived needs at each stage of my life.
Sure, governments can make protectionist rules to prevent or dissuade me from spending my money as I choose, but then another rule that really matters - the law of unintended consequences - will make the cars they want me to buy progressively less attractive in direct proportion to the extent that government protects their manufacturers from competition. I am pretty sure protectionism is what made the French chapter of my car history such a disaster.
As Peter Lilley is quoted as saying in the linked post by Mark Wadsworth;
"Britain set the rules of tennis but rarely wins Wimbledon. British exports to the EU have grown less rapidly since the Single Market than they did before, less than our partners’ and much less than non-EU countries’ exports! Maybe that is partly because we suffer EU regulations on 100 per cent of our companies whereas non-EU firms need only comply with EU regulations on activities carried out within the EU."
Quite. So enough already with the "trade deals" crap. I respectfully suggest you don't allow all the hot air about them to influence your vote in the Referendum. And if you can't name all of the EU's Presidents without recourse to Google and explain precisely how to get rid of the rascals if you are dissatisfied with them, then I respectfully suggest you are not morally entitled to vote "Remain".