LONDON — The proposition that Britain could have its cake and eat it during Brexit, as the foreign secretary Boris Johnson once said, was always dismissed as a fiction by opponents. On Wednesday, it was quietly interred by the government as it capitulated on the amount it will have to pay for a divorce settlement.

And this was not Britain’s first capitulation over Brexit, nor — almost certainly — will it be the last, analysts said.

What Mr. Johnson was saying was that Britain could secure the economic benefits of membership in the European Union without paying a penalty or being subject to its rules, particularly on the free movement of labor within the bloc.

On Wednesday, Britain reportedly agreed in principle to a divorce check of around $47 billion to $53 billion in the hope of securing the start of talks on a future trade arrangement with the 27 nations.