LONDON, England (AP) — Politicians who wanted Britain to leave the European Union were not shy about making promises. They plastered their campaign bus with vows to “take back control” on immigration and boost funding for the beloved National Health Service.

But with Britain facing months or years of negotiations to detach itself from the 28-nation bloc, victorious “leave” leaders will find their pledges of prosperity, sovereignty and more public spending hard to keep.

They know it, and are already lowering expectations.

Conservative “leave” supporter Iain Duncan Smith now says the campaign had not laid out promises but simply “a series of possibilities”. And having shocked the world — and global markets — with the referendum result, Britain appears in no hurry to rush out the EU’s exit door.

The “leave” campaign, led by former London Mayor Boris Johnson, has yet to lay out what it thinks Britain’s future relationship with the EU should look like, and Prime Minister David Cameron says Britain won’t trigger formal divorce talks until a new prime minister is in place after the summer.

Before Thursday’s referendum, however, the “leave” side’s tone was considerably less ambiguous: They wanted out, they wanted control of EU immigration and they wanted a lot of money back from the EU.

“Let’s take back control,” said a slogan on the “Vote Leave” bus that traversed the country, as its leaders argued that Britain could secure its borders and limit EU immigration only by exiting the bloc, therefore eliminating the right that EU workers have to live and work in Britain.

An estimated two million Poles have come to work in Britain since 2004, and 850,000 are still here.

Another bus-side “leave” pledge said: “We send the EU 350 million pounds a week — let’s fund our NHS instead”.

Many economists think there’s a conflict between the key promises of reducing EU immigration and producing a flourishing economy. They argue that Britain needs access to the EU’s tariff-free single market of 500 million people, and won’t get it if it tries to restrict the free movement of EU labour.

Jonathan Portes, principal research fellow at the National Institute of Economic and Social Research, said anti-EU campaigners chose to ignore the link between economic access and EU immigration in order to win votes.

“They told lots of people that these trade-offs, which were reasonably obvious and are now coming to the fore, didn’t exist,” Portes said. “Sooner or later they will have to deal with it.”

The desire to curb immigration motivated many “leave” voters, since more than three million people born in other EU nations now reside in Britain. An estimated 1.2 million Britons, including many retirees, have moved to other EU nations, but Britain’s relatively thriving economy has meant that immigration has far outstripped emigration in recent years.

Many Britons who voted “leave” believe those EU immigrants have placed strains on schools, hospitals and housing, even though they have paid taxes and many economists argue that immigrants are an economic boon.

Leaving the EU would allow Britain to “take back control” by renouncing the free-movement principle. But if it did, it would be unlikely to get open access to the EU’s single market, with which the UK currently conducts half its trade, exporting everything from beef and lamb to financial services.