“Theresa May needed to bring some Brexiteers into the government in order to protect herself and to counter the charge that she is a closet remainer,” said Simon Tilford, the deputy director of the Center for European Reform, a London-based research institute, noting that she had argued to stay inside the European Union, albeit rather tepidly.

“But the risk is that this prolongs the very high degree of uncertainty over the British economy, that we see relations deteriorating with other countries, and that this militates against negotiating a deal,” he added.

While Ms. May promises to deliver Brexit, she speaks with more passion about her domestic agenda. On the steps of 10 Downing Street on Wednesday, she said that she would lead a battle against “burning injustice” and help create opportunities for all, not just a “privileged few.”

She wasted no time in dispensing with the services of George Osborne, the former chancellor of the Exchequer and the architect of public spending curbs, and appointing new faces to domestic ministries: Amber Rudd at the Home Office, and Justine Greening at the Department of Education.

However, Mr. Osborne’s replacement, Mr. Hammond, who must find the money for any new social spending programs, “has a reputation as a fiscal hawk, which potentially conflicts with May’s pledge to ease up on the pace of austerity,” said Kallum Pickering, the chief economist for the United Kingdom at Berenberg, an investment bank.

Mr. Hammond on Thursday highlighted the importance of resolving Britain’s new relationships with the European Union, telling the BBC that “if there is one thing that is damaging our economy today — right now — it is uncertainty for businesses.”

Mr. Hammond made a special plea on behalf of London’s financial services sector, a prominent part of the country’s economy and a huge generator of tax revenues that finance social spending.

“We have to make sure that in our negotiations with the E.U. we have very clearly in our minds the need to ensure access to the European Union single market for our financial services,” he added.

The French foreign minister, Jean-Marc Ayrault, urged Britain to quickly begin the process to leave the European Union, saying, “We cannot let this ambiguous and murky situation last, in the interest of the British themselves, I would even say.”

But that may not be the priority of David Davis, a veteran lawmaker and former Europe minister, who will head up a new ministry responsible for Brexit, or of Liam Fox, who will be in charge of negotiating international trade deals.

Mr. Davis seems to be gearing up for a war of attrition with other European Union nations. In an article on the Conservative Home website, published this month, he suggested that Europe would ultimately buckle and give Britain continued tariff-free access to the single market.

“Once the European nations realize that we are not going to budge on control of our borders, they will want to talk, in their own interest,” he said.

Yet European leaders have made clear that they do not intend to give way to Britain’s demand that it get unimpeded trading rights with the Continent without adhering to the bloc’s immigration rules, which require member countries to let European Union citizens live and work where they wish. That open-borders policy, as much as any other factor, drove British sentiment against the bloc.

As a result, the uncertainty could drag on for some time if Ms. May’s negotiators are not willing to reach a compromise on immigration, potentially hurting the economy and giving other nations time to poach British business, not least from among banks and investment firms that are now considering moving some operations away from London.

Mr. Tilford argues that the main pro-Brexit campaigners are ill equipped to negotiate, saying that they lack understanding of how the European Union works, what trade-offs are required and, therefore, of what deals are possible.

He pointed to some of Mr. Davis’s Twitter posts that called for “a UK-German deal” allowing access to Britain for German cars and other goods in exchange for a deal on British exports, and claimed that “similar deals would be reached with other key EU nations.”

In fact, the European Union reaches trade agreements as a bloc, rather than on a country-by-country basis, so Germany would not even negotiate directly with Britain.

But Mr. Tilford said that there might be “method in the madness” of Ms. May’s central pro-Brexit cabinet appointments.

“They are going to be confronted by the reality,” he said. “It won’t be possible for them to continue to claim that you can have your cake and eat it. They are going to be negotiating with other countries, and they will no longer be able to rely on bluster and obfuscation.”

Mr. Tilford said that if ideological supporters of Brexit failed or were discredited, that would force a reality check on their supporters, leading to a more flexible negotiating stance.

Even under this scenario there is a hitch, however: the economy. “In the short to medium term, things can get a lot worse,” Mr. Tilford said.