Once British politicians stop double-crossing each other, a tougher foe looms

"It's the EU and not Britain that has the upper hand here," said Agata Gostynska-Jakubowska, a research fellow at the London-based Centre for European Reform.

Both Europe and Britain would be hurt economically if the two sides can’t reach a deal, she said. But Britain, as the smaller market with more direct dependence on Europe than the other way around, would be hurt more.

Giving the Europeans even greater firepower is the ticking two-year clock on the process once Britain gives formal notice it is leaving the EU, after which it would be kicked out of the union whether or not a new deal is in place.