There certainly is conflict. The same economic theories that lead to the conclusion that low tariffs are good place the same importance on the free exchange of

There certainly is conflict. The same economic theories that lead to the conclusion that low tariffs are good place the same importance on the free exchange of goods as the free exchange of labour. The treaty of Rome is the governing treaty in the EU in this respect and it has provisions on both. Since it is precisely the free exchange of labour that the UK wants to eliminate, they will need to violate the treaty and lose the free exchange of goods. How this will affect the application in the UK of existing trade agreements between external countries and the EU is another question. Since the bureaucratic process of bringing goods to the UK will be different than bringing it to the EU, foreign countries will likely take the stance that those trade agreements no longer apply to the UK.