We're the EUs most important customer, certainly in the case of France and Germany. We are a relatively rich, geographically close economy, who are paying full whack for their expensive luxury goods, (eg cars and champagne). This makes it extremely important for them that they don't piss us off, and economic suicide for them to engage in some sort of trade war with us. Tariffs hurt them in two ways, because they risk alienating a really important market (will the British people continue to buy their stuff if they are seen as responding vindictively to a democratic vote) and their goods become more expensive than their competition. French farmers and German car manufacturers would be in open revolt if this was even suggested, and the Eurozone would be plunged into an even deeper crisis. It aint happening.
This seems to me to be remarkably similar to the argument expressed by Tsipras and Varoufakis when trying to persuade the Greek people that they would be able to lead them out of austerity. In that case it was German financiers, fearful of another banking crisis, rather than German car manufacturers, who would force Merkel to back down and hand the Greeks a bail out free from austerity measures. Varoufakis' had this quaint belief that he was an expert in Game Theory and that that when push came to shove the EU would back down.
As it turned out, the German financiers had much less influence than Varoufakis expected. Fears of another banking crisis were offset by fears that a favourable bail out would tempt other countries to default. The German people were overwhelmingly against giving Tsipras what he wanted, Tsipras and Varoufakis also under estimated the hostility to Greece of the smaller countries, those that weren't required to contribute to a bail out, but who resented the idea that Greece would escape austerity when they had pushed through their own deeply unpopular austerity programmes.
In the end the Greeks got their bail out extended, just as the UK will get a trade agreement. But it was nothing like as favourable as Tsipras and Varoufakis had promised. It isn't going well, the Greeks are still protesting on the streets of Athens. And Varoufakis is advising Jeremy Corbyn.