NEW YORK — If Theresa May thought she was constrained by Brussels, just wait until Donald Trump gets involved.

While the U.S. president continues to talk up the prospects of a "great" trade deal with the U.K. once it leaves the European Union, officials in Washington say the U.K. must leave open the prospect of deregulation once it's out of the EU in order to make the most of a deal with America.

The U.S. is "trying to help the U.K. do whatever it can to have a successful Brexit," a senior U.S. official told Washington reporters during a briefing on the administration’s trade agenda last week.

"At the same time, we are encouraging them to make sure that any deal that they agree to [with the EU] preserves enough space on regulations and things like that so that we can get the benefits of an [free-trade agreement]," the official said.

U.S. pressure on trade comes at a risky moment for the British prime minister, who flew to New York Tuesday for the United Nations General Assembly and will meet Trump on Wednesday. Her trip follows a fractious week in Brexit negotiations in which EU leaders said her Brexit strategy would not work, emboldening critics within her own party who have sought to present her Brexit plan as a sellout.

The U.S. president previously raised concerns that May's EU plan could kill off a U.K.-U.S. trade deal.

Central to much of the criticism of May's proposals is that they would leave the U.K. shackled to European rules covering goods, and therefore, Brexiteers say, leave Britain unable to strike ambitious trade deals elsewhere in the world and reap the rewards of Brexit. Hints at similar concerns from across the Atlantic could hardly have landed at a more problematic time for the prime minister.

In response to a question from POLITICO on board an RAF Voyager plane on her way to New York, the prime minister said she would be able to maintain frictionless trade and strike “good, improved trade deals” with countries around the rest of the world.

“Just think about this: If having those EU regulations stopped good trade deals, how come the EU has done trade deals with countries around the rest of the world?” May said.

“We will be able to do trade deals around the rest of the world. We are taking a decision, we are proposing that frictionless trade and that important cross-border trade continues to be good today with the EU and as seamless as it has been in the past, that is important for jobs and businesses in the U.K.”

'Crazy' Chequers

But her critics maintain her plan is flawed.

"This explains why Chequers [May's proposal for a deal with the EU, named after her country retreat where the Cabinet approved it] does not work as it fails to leave the regulatory freedom needed to make deals elsewhere," said Jacob Rees-Mogg, leader of the backbench Brexiteers in the U.K. parliament. "It is helpful that U.S. officials are making this clear."

"U.S. trade people think Chequers is crazy," said Tory Brexiteer Bernard Jenkin. "Because it cuts us off from dealing freely with the rest of the world. We need regulatory freedom on goods so the U.K. can dismantle non-tariff barriers amongst good regulations in exchange for access for our service sector, which is 90 percent of our economy."

A report by the Institute of Economic Affairs think tank published Monday, and backed by leading Brexiteer and former Brexit Secretary David Davis, devotes a whole chapter to "Why the Chequers Proposal Removes Independent Trade and Regulatory Policy."

Another former minister, who declined to speak on the record, said the prime minister should be "much more honest" that free and frictionless trade with Europe requires the U.K. to remain "pretty much in lockstep" with the EU.

"By doing so it obviously diminishes considerably, if not entirely eradicates, our ability to negotiate a broad FTA with any other third country, including the U.S.," they said.

Trumped

The U.S. president has previously raised concerns that May's EU plan could kill off a U.K.-U.S. trade deal.

He backtracked on his comments to the Sun in July after a meeting with May, describing her as a "very tough negotiator" who is "doing a fantastic job." He added there could be a "great" trade deal between the U.S. and U.K. at a joint press conference.

Since then, however, little visible progress has been made beyond the creation of working group between trade ministers on both sides that is working to lay the groundwork for a future deal.

U.S. trade experts say the issue is more one of capacity than lack of interest, with the White House and the U.S. trade office consumed by crises ranging from the trade war with China to renegotiating NAFTA. Throw in the fallout from steel and aluminum tariffs and a new dialogue with the European Union, and trade officials are facing a perfect storm of distractions keeping them from focusing on anything but Britain.

"I think [a U.K.-U.S. trade deal] is something that’s incredibly popular with our Congress. USTR [the Office of the United States Trade Representative] is behind that. So that is something that we will eventually do," the U.S. office said.

A spokesman for the U.K.'s Department for International Trade said it is committed to securing "an ambitious free trade agreement with the U.S. that is consistent with our future relationship with the EU and our domestic priorities." It is currently holding online consultations about how to approach the negotiations.

Whose standards?

However, trade experts and food industry figures remain cautious about what the U.S. might demand in return for a free-trade agreement.

There are also warnings that potential lower tariffs may be offset by the administrative costs of running two tariff regimes at the U.K. border under May's Chequers plan.

Katie Doherty, policy director at the International Meat Trade Association, said she welcomes the principle of a U.S. trade deal but it is "difficult to envisage" that it could be achieved without the U.S. wanting "recognition of their different practices," which she said could endanger exports to the EU that account for 75 percent of her industry's trade.

Any divergence on the type of product that the U.K. accepts for import, for example hormone beef, would make it less likely that veterinary checks between the EU and U.K. could be avoided, Doherty said.

British Trade Secretary Liam Fox has repeatedly insisted "there will be no lowering of U.K. food standards" in future trade deals.

David Henig, a former U.K. trade official who was involved in U.S.-EU trade negotiations, agreed that a shared rulebook with the EU could cause problems for the U.S. trade deal, although it may not be terminal.

“The U.S. agriculture people need to be able to export, they insist on their standards for export," he said.

Nick Allen, chief executive of the British Meat Processors Association, said the U.K. has particularly high animal welfare standards and very prescriptive hygiene standards, and anything that means they have to compete with lower standards is a problem for them.

Nevertheless, Trade Secretary Liam Fox has repeatedly insisted "there will be no lowering of U.K. food standards" in future trade deals.

Sam Lowe, a senior research fellow at the Centre for European Reform, said the idea of the Chequers plan is that the U.K. would run two tariff regimes at the border — the EU's and the U.K.'s.

The importer would pay the higher tariff, but could claim the lower U.K. tariff only if the final sale of the product is within the U.K. To claim the lower tariff, the importer could either join a new trusted-trader scheme, which would mean regular supply-chain audits, or it could pay the EU tariff, and then claim the duty back upon proof of sale in the U.K.

Lowe said the proposal would "reduce the likelihood of importers making use of the lower U.K. tariff on imports from, for example, the U.S., as the administrative burden is higher."