London (CNN Business) Long before the United Kingdom voted to leave the European Union , British Euroskeptics were fond of claiming that Brexit would turn the country into an independent, free-trading nation. The crown jewel of trade deals, they argued, would be with the United States.

It's easy to see why this idea is popular among Brexit supporters. The United States is not only the United Kingdom's single largest trading partner, but also the biggest economy on earth. Why wouldn't a buccaneering, free-trading Britain want to escape the shackles of the European Union and sell goods to its free-spending, closest ally?

US President Donald Trump sounded enthusiastic about such an outcome only last week, claiming the United Kingdom, once free from Brussels, would be able to do four or five times more trade with the United States.

There was a catch — Trump said this could not be done with the Brexit deal Prime Minister Boris Johnson recently negotiated with the European Union. Indeed, he said that Johnson should not only abandon the deal, but take the controversial step of working with Nigel Farage, leader of the Brexit Party, which favors leaving the European Union without an agreement.

Doing so would theoretically allow the United Kingdom to strike a quick, fruitful trade deal with the United States. Some inside the UK government believe that this alliance would sharpen minds in Brussels too, nudging the European Union to finally break and grant the United Kingdom a trade agreement of its own, on London's terms.

So, the United Kingdom would have two free trade deals signed in record time, proving to the gloomsters that Brexit can be a huge success after all. When Trump spoke to Johnson on Tuesday, he expressed a desire to strike a "robust" free trade agreement once the United Kingdom leaves the European Union, according to the White House.

If it all sounds too good to be true, it is. Rather than walking into a sweetheart deal with the United States, the United Kingdom is likely to be confronted by a phalanx of hard-nosed American trade officials who will attempt to pry open British markets to more American goods. Any deal would need to be ratified by the House of Representatives, a body currently controlled by Democrats who are concerned that Brexit could undermine the Good Friday peace agreement on the island of Ireland.

And the more one examines what any trade deal could possibly look like, the less attractive it looks for the United Kingdom.

Striking a deal

The United States, famously, drives a hard bargain in trade deals. "They know that pound-for pound, access to their market means more to you than access to your market means to them," explains Dmitry Grozoubinski, a former Australian trade negotiator and founder of ExplainTrade.com.

The United States also holds all the diplomatic cards. As Allie Renison, head of European and trade policy at the Institute of Directors, told CNN Business: "It's rarely the one prioritizing a deal in the first place; other countries often want access to the US market for political reasons and see it as an expression of alliance."

All of which means that the United States starts any negotiation from a position of strength.

This creates an immediate problem for the United Kingdom. America, which already has a trade surplus with the United Kingdom, is not about to grant a trade deal that showers money on the United Kingdom without asking for a lot in return. And Washington's demands may not be palatable, most notably on agricultural goods, including food, and health care.

"The US's priorities would be quite difficult for the UK to take on board because they focus on agricultural goods and medicines procurement," says Sam Lowe, a senior research fellow in trade at the Centre for European Reform.

These demands play into the hands of people who oppose the idea of a trade deal with the United States, as they confirm their two greatest fears.

Lowering standards

Take food standards. In this area, Europe's regulations are generally accepted as being stricter than those in the United States, and American trade negotiators would doubtless seek to remove some of these barriers in order to sell into the UK market.

But this is politically troublesome in the United Kingdom. Britons are very uncomfortable at the idea of being served chlorine-washed chicken or hormone-treated beef. As the UK general election campaign gets underway, opposition Labour Party leader Jeremy Corbyn used his campaign launch speech to say that Johnson's Conservatives would put chlorinated chicken on UK supermarket shelves and "slash food standards" to match the United States, where there are "acceptable levels of rat hair in paprika and maggots in orange juice."

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And any dilution of food standards in the United Kingdom would have wider implications for any trade deal that it could strike with Europe, given that chlorinated chicken is banned in the European Union.

Then there are EU animal welfare standards. In the United Kingdom, animal welfare is a big deal. The prospect of flooding the country with produce from battery hens or farms that allow bad things to be done to cute animals would not be popular.

A fight over the health service

But the skirmishes over food standards would be nothing compared to the political warfare over Britain's revered National Health Service, which provides health care free at the point of delivery but which has been straining at the cost of doing so.

A central plank of the Labour Party's election campaign is a claim that Johnson is ready to sell off the NHS to Trump.

It's a powerful message, even if it's not strictly true. The United States does not particularly want to run British hospitals. The real argument with the United States would be over how the NHS procures medicines from private drug companies.

American drug companies can already compete for NHS medicine procurement contracts. But Washington thinks that other governments put pressure on pharmaceutical companies to charge below the market value for their drugs. In any trade negotiation with the United Kingdom, the way in which the country assesses a fair price for drugs would likely be on the table.

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As Lowe explains, when Washington negotiated its trade deal with Seoul, it "managed to get South Korea to agree that US companies could challenge fair value of medicines." A similar outcome in any deal with London would mean more expensive drugs on the UK market.

Perhaps sensitive to the political damage this attack line could cause, UK government ministers have lined up to rule this out. One, Michael Gove, told the BBC this week the government had "made it perfectly clear drug prices won't be going up".

This might be the aim, but in reality, until the negotiating teams sit down to talk, it's not really for him to say.

But what if there was a deal?

Let's say the United Kingdom, buoyed by its historically close relationship with America and supercharged by Johnson's personal chemistry with Trump, manages to clear these hurdles. What then of Trump's claim that trade could increase four- or five-fold?

It's hard to see exactly where the demand for this additional trans-Atlantic trade would come from. As Grozoubinski explains, the United Kingdom has yet to identify any "lucrative or identifiable asks" of the United States in nearly three years of searching. "The US is already a fairly open economy in the areas it's willing to be open in. Trade agreements are fundamentally about removing barriers to trade. For Trump's claim to be true, there would have to be vastly more barriers to UK trade than there are."

And in any event, it's worth repeating Trump's claim that a deal could only happen if the United Kingdom walks away from Brussels with no deal. What could that mean?

A disorderly exit could very easily lead to both food shortages and an increase in medicine costs. The United Kingdom imports more goods from the European Union than it sells. The United Kingdom would still need those goods, so there would be an immediate impact. Lowe says the British pound would weaken against the euro, making it more expensive for Britons to import products from eurozone countries.

While a trade deal with America would open the United Kingdom up to a wider range of goods, the unpredictable cost, quality, and sheer length of time it would take to get them here makes the deal look increasingly unattractive to politicians.

The import problem extends beyond consumer goods. The Royal College of Radiologists has repeatedly expressed concern about the impact delays could have on the effectiveness of materials used in the treatment of cancer.

What about exports?

The primary concern for British businesses after Brexit is how easily and cheaply they can sell their products abroad.

Leaving the EU single market and customs union would create problems for supply chains and a headache for exporters. "It makes a lot of sense for a company to build half its product in Poland, a quarter in Germany then finish it in the UK before shipping the whole thing off around the world, because those borders basically are not there," says Grozoubinski. "After Brexit, that probably won't make sense anymore for a lot of manufacturers."

New trade barriers with the European Union would encourage Japanese carmakers who have built huge factories in Britain to take their business elsewhere . Honda is planning to shut down a major factory in England that employs 3,500 people, and Nissan has scrapped plans to build certain models at its massive plant in Sunderland.

The United Kingdom exports far more services than it does goods. As things stand, an insurance company based in London can sell a product to a customer anywhere in the European Union and be treated exactly the same as a services company from that nation.

However, under World Trade Organization rules — which would kick in as soon as the United Kingdom left the European Union if no formal deal is in place — it is perfectly legal to obstruct a third party operating in this way.

And while the European Union might not want to cause overnight chaos, it could turn off the United Kingdom's services tap. "After Brexit, the EU has every incentive to say 'hey, Dublin, Paris Frankfurt would like to have people with a lot of money to eat in their restaurants," explains Grozoubinski. "Why should we continue providing the UK high preferential access when it's made clear it wants to do so on quite violent terms?"

It's currently easier to trade services across the European Union than it is across US state lines. Which is why the United States cannot offer the United Kingdom all that much on services. "The US services market isn't very complete and lots of the regulations are done at a state level," says Lowe.

So why would the UK consider it?

Given all the problems that prioritizing a trade deal with the United States could cause — from unpredictability in food supplies to economic chaos — why would a UK government even entertain the prospect of it?

Along with the hard-headed reasons that some voted to leave, there was a lot of romanticism about the United Kingdom claiming back its status as a sovereign nation. A quick trade deal with the United States would be a huge political trophy for a British leader.

And many Brexit supporters sincerely believe that a trade deal with the United States will only result in positives for the United Kingdom.

As Shanker Singham, a pro-Brexit competition and trade lawyer, told CNN Business, a trade deal "could lead to substantial benefits for the United Kingdom. He says that the country "should want a comprehensive [free trade agreement] with the European Union and also a comprehensive deal with the United States," noting that "many countries do have both deals now." He also claims that "the NHS would actually benefit from more open competition."

But the road to striking that deal is treacherous. After swallowing all the US demands, the UK government will have spent a lot of political capital. And not just at home: accepting these concessions will make any future arrangement with Europe very difficult.

Prioritizing an ally who makes you do things you don't want over your nearest trading partner in exchange for a deal that will leave you poorer is very strange domestic politics. But three years of Brexit paralysis has left the United Kingdom in a strange place.

It needs to prove that it can leave the European Union without causing itself too much damage. Unfortunately, the way to do this doesn't appear to be snuggling up to its closest ally.