Not really, we could just drop tariffs on items we're struggling with supply of and advertise that we're buying. We literally can selectively import wtf we like with no tariffs if we want when outside the EU.
As big and scary the export numbers sound its estimated that less than 10% of UK business exports, and even less of those to the EU. Even with tariffs we would still export to the EU and whilst supply and demand laws would suggest the higher prices caused by tariffs would slow demand, there's no guarantee we actually would have much higher prices if we manage imports well and don't slap punitive tariffs on everything.
Also the Eu has free trade agreements with other countries who have totally different market regulations, there's no reason other than spite why a trade agreement cannot be struck with them when we currently have regulation parity.
Coffee for instance, beans have no tariff applied by the EU but HUGE tariffs applied if they are roasted. We are all paying through the nose for roasting whilst keeping a foot on the head of coffee growers in countries that could really do with being able to expand their industries.
You think Britain on its own is as attractive a proposition to other countries as the EU so they would replicate the same agreements you were part of before in a new partnership "just cos"?
British exceptionalists make me LAUGH.