The first thing to point out is that trade agreements work both ways. When Brexiters state 'they will still want to sell us their cars' - a reference to VW, BMW, Renault, Fiat and Mercedes putting pressure on the EU to keep trade flowing - the only reason they might face tariffs will not be because of the EU mandating 'punishing' taxes, but the UK's own customs imposing them. It's the importing country who 'fines' other nations' exporters. In other words, if VWs etc attract tariffs, it's because the UK government applies them to force Brits to buy British cars.
So when they try to make VWs and BMWs more expensive for British citizens to buy, that's not going to make them popular at home. It's not going to happen. Brits will continue to buy their French, Italian and German cars without being fined by their own government. That's called shooting ourselves in the foot. If BMWs etc weren't already being sold here, then perhaps tariffs might be considered. But we've been buying and desiring them for donkey's years.
Whether the EU make British cars more expensive or not, is for them to decide. Frankly they probably will - and who in the EU will give a damn? They've got plenty of choice over which cars to buy other than British ones. We don't.
But the claim by 'my side' I need to challenge most is that when we leave in March 2019, we will immediately fall outside the existing FTAs the EU has already negotiated, and that this will hurt. The numbers of countries claimed that we will no longer have FTAs with has variously drifted from 50 up to 75 and somewhere I even read over 90. The fact is about 85... but what we're not told is who these FTAs are with. And the truth is, they're not worth bothering about. Nearly all want to sell us stuff. We sell them all very little indeed.
Here's the list of all nations the EU has FTAs with (35), have agreed but not signed (50), or are still negotiating (12). These exclude nations like the USA and China with which the EU has no trade agreements. Sounds a lot, but the vast majority are small third world countries who don't buy anything from the UK anyway. All the big trading nations are either in the EU or don't have FTAs with the EU.
So despite wanting to wave the 'we'll lose all our FTAs' flag, the reality is the only FTA that matters is the one with the EU, and they're not going to give us one. And the UK won't impose unpopular tariffs on EU imports as a tit for tat, so we've got nothing to negotiate. Which is why I'm a Remainer.
Oh and if you're screaming at the screen 'what about our sovereignty?', I challenge you to name one law we don't want that's been imposed on us. That's one sodding law in 43 years of membership. Can't? Perhaps that's because we helped determine them and could veto those we didn't like, and because their purpose is to raise standards everywhere in the interests of safety, fairness and equality. But we Brits know best.