Only a year ago, the vote on European Union membership had seemingly divided the country along clear lines between “Leave” and “Remain.” The vote on Thursday erased such clarity, delivering mixed messages, even as Britain remained deeply split — by region, by class and by generation.

For the past year, the extent of the debate about the exit from the European Union in Britain has been limited to vague promises of repatriating British funds from the European budget, controlling immigration and negotiating a favorable trade deal. Britons have heard little about the cost of leaving the world’s biggest free-trade bloc — not least the tens of billions of pounds owed to Brussels for existing liabilities such as pension obligations and investment commitments in the current European Union budget.

“The British public have not at all been prepared for having to pay a large check to Brussels to settle our debts in this divorce,” said Peter Ricketts, a former ambassador to France and now an independent lawmaker in the House of Lords, Britain’s upper chamber.

Mrs. May had told voters that she wanted to start negotiating a trade deal straight away — something that has been categorically ruled out by the 27 countries on the other side of the table. They have been clear that they want to talk about a divorce settlement first: about the rights of European Union citizens in Britain, and of Britons in Europe (doable, officials say); about the border between Northern Ireland and the Republic of Ireland, which remains a member of the bloc (trickier); and about the most contentious issue in any divorce: the money.

Only when “sufficient progress” has been made on these issues, the European Union says, can the talks move on to hammering out a framework for a future trade deal and to designing a transitional agreement that would bridge the end of British membership in the bloc — due to formally expire in March 2019 — until a final deal is ratified by all 27 remaining member states.

Even before talks have started, the trust level is at rock bottom. A dinner Mrs. May had with the president of the European Commission, Jean-Claude Juncker, was leaked in astonishing detail to a German newspaper by Mr. Juncker’s team. The leaks were widely condemned by officials — but their content was described as accurate.