@ JohnMangan & loudspeaker:
If this is what you believe, then you've been lied to.
The UK has finalised trade deals for 164 countries (99.6% of global cross-border trade) for 2019.03 for all but (IIRC) 14 line-items in 19 countries, and even those are scheduled to be finalised by 2019.06, and those are only those unusual goods on which MaximumDiscount-Quotas have been set. For example, Australian cheddar cheese. Yes, I'm afraid post-Brexit, you in the UK won't be able to tuck into any less-than-full-tariff Aussie cheddar cheese for 3 months. But then, you haven't actually imported any since at least 2013 so this hopefully will not bring your society to its knees in flaming ruin, eating your own babies for warmth.
UK is a member, as is every EU country, as is the EU itself.
By virtue of achieving membership, the UK has trade-deals with all 160odd members. Nearly all of your time spent "earning" membership, IS the negotiation of exactly those trade deals.
There is absolutely nothing to stop any country & UK trading. Even with the 0.4% trade-volume with NO TRADE DEALs ARRRGGGHHH..ARRRMAGEDDON. For example, the EU traded with all the WTO countries for 12yrs despite technically having NO trade deals with them because their WTO membership was void/invalid. Non-EU countries are quite pragmatic -- they're willing to trade as if your standard global trade deal was in place, until it is.
Again, you are confusing SpecialMagicWonderTreatmentJustForYou with "trade deal".
EU trade is NOT the majority, it is slightly less than half; 47% if you're looking at Imports which is what all the Food!Medicine! panic seems to be about.
Re Imports: yes this slow-down will be a factor for the duration of re-resourcing the border, re-establishing what you used to have. Again, not armageddon as you are presenting it: just a process slow-down causing serious bottlenecking and queuing. But again, there's nothing requiring the UK to go full-throttle straight away. They could announce "Carry On While We Prep" and continue waving everyone through for say 6mths, then with the larger lorry parks and more inspection sites and more staff and so on, switch over then. Zero drama.
Re Exports: well this COULD be a problem. Because the EU has acted like a prick from the outset, deliberately finding any way to stuff the UK then being obstructive, and I don't expect this to change any time soon for the EU-bureaucracy or for France. Specifically, UK export goods getting stuffed round in EU Customs.
So the actual Brexit losers are potentially the food exporters getting perishables delayed too long in French customs.
Within a couple of weeks they'll just switch to Rotterdam, Esbjerg, etc. Maybe an opportunity for Husum etc. to become major ports again :)
If your description were correct, then the EU could not trade the way it does, because it and all its members are members of the WTO. Likewise NAFTA=nono. Etc.