Even then, he added: “This was the easy part, but now the British cabinet has to confront some real choices. Now, we get to the really divisive part about what kind of future trading relationship we want with Brussels.”

That debate boils down to two opposing sides: those who want the closest possible future relationship with the European Union for the sake of trade and business ties, and those who want a sharper split, so that Britain can freely negotiate trade deals with countries like the United States and Australia without being hampered by allegiance to all of the European Union’s regulations and standards.

The problem for the British government is that it is no closer to deciding the matter than it was when Mrs. May invoked Article 50 in March, initiating the process of withdrawal, or Brexit.

Mrs. May has declared only that Britain would not seek to remain a member of the single market or the customs union, while also saying that she wants the best possible trading relationship with Europe, which is, after all, where most of Britain’s trade goes.

Simon Fraser, a former senior British diplomat who runs a consulting company that focuses on Brexit, said that “Britain wants to move quickly to phase two, but in fact it does not have a policy for phase two.”

Brexiters argue that Britain is so important to Europe that London should be given a special or “bespoke” deal, given the 44 years of bloc membership. But the European Union is legalistic, bureaucratic and runs by precedent. And there are only a limited number of templates for a future relationship, Brussels officials consistently say.

Britain could work out a deal, much like Norway has, where it remains a member in everything but voting power and name — trading freely but subject to freedom of movement and labor for European Union citizens and continuing to pay into the union’s budget. That seems unacceptable to Britain, which voted to leave in large part to stop freedom of movement.