According to the OEC, the UK is the 10th largest exporter in the World, but only 21st by population. I'd say that the UK is "punching above its weight".
The UK not only exports to the EU, but imports as well. Ultimately, if Brussels wants to risk losing a huge amount of jobs and commerce within the EU (by ceasing trading with the UK), then that's not going to make them very many friends is it?
How do you think the Spanish (who have a huge market growing fruit/vegetable produce for the UK) are going to react when those business close because Brussels screwed up negotiations? Spain is a basket case already - putting thousands of Spaniards out of work just to be bloody minded to the UK will be disastrous for the [Spanish] economy.
The German auto industry is already lobbying Merkel to get a good deal - they don't want to lose the UK market (especially as Trump has just imposed large import tariffs on them).
The UK's trading relationship with the rest of the EU is not a one-way street. So, yes, there is a lever.