'Tooth fairy' or 'disaster'? UK's Brexit gamble on Trump

London (AFP) - Hailed last week as an ace up the sleeve for Britain in the upcoming Brexit negotiations, relations with US President Donald Trump are turning into a diplomatic headache for Prime Minister Theresa May.

Trump's rejection of the European Union and his enthusiasm for a swift post-Brexit trade deal with Britain appeared to boost May, demonstrating that she had other options if EU leaders offered an unattractive deal.

"Trump has come along like the tooth fairy, this is one massive, magnificent gift," one Brexit-supporting MP told the Spectator magazine last week.

The bond between the two leaders was reinforced on Friday when Trump hosted May in the White House, and pictures of them holding hands were splashed over the front pages of Britain's newspapers.

But instead of arriving home to plaudits, she flew into a firestorm as Trump announced a temporary measure preventing refugees and travellers from seven predominantly Muslim countries from entering the country, sparking global protests.

May initially refused to condemn the move, but then issued a statement saying she did "not agree", highlighting the peril of pinning her fortunes on the US president in the eyes of some commentators.

"The election of Mr Trump has transformed Brexit from a risky decision into a straightforward disaster," wrote Financial Times columnist Gideon Rachman.

"The emperor Nero has now taken power in Washington -- and the British are having to smile and clap as he sets fire and reaches for his fiddle."

- Queen dragged into row -

The diplomatic tangle is further complicated by May inviting Trump for a state visit later in the year, when he will be hosted by Queen Elizabeth II.

More than 1.7 million people have signed a parliamentary petition demanding that the trip be downgraded over concerns that he will damage the reputation of the highly popular queen.

The petition is to be debated in parliament on February 20.

"Anything that embarrasses the queen plays badly in British politics," said London School of Economics (LSE) professor Iain Begg.

Scaling down the visit would also likely go down badly with the US leader, who has spoken of his admiration for the British monarch.

May "doesn't want to upset Trump... and he will be watching how she behaves very carefully," LSE fellow Brian Klaas told AFP.

"She will have to be very careful."

Teaming up with Trump was therefore a "political risk," said Begg, drawing a comparison with former prime minister Tony Blair, who was branded George W. Bush's "poodle" during the 2003 Iraq invasion.

"She's not tied to him yet but she has started tying the knot," Klaas said. "She can untie it, but right now, the picture of them holding hands is one that's not easy to distance yourself from."

- Anti-establishment rage -

There is also no guarantee that any eventual trade deal with the United States will boost Britain's economy, particularly given Trump's "America First" policy against free trade agreements.

"May is caught in a dilemma: she wants something quickly because it will look impressive to those worried about her negotiation strategy but she needs to get something good so she doesn't get criticised for being soft," said Begg.

May will ultimately be judged by the British people, and has plenty of breathing space with the next general election not due until 2020.

Ties with Trump may also play well with many voters in a country where immigration and anti-establishment anger were key issues in the decision to leave the EU.

A YouGov poll published Wednesday found 49 percent of Britons thought the state visit should go ahead, compared to 36 percent who wanted it cancelled.

Meanwhile 50 percent thought Trump's refugee ban was a bad idea, but 29 percent approved.

Trump has credited Brexit with paving the way for a popular revolt against the establishment, which could also give May leeway in their relationship, Klaas added.

"He wants to repay Britain... as a way to say 'well done, good job'," he said.

The relationship will therefore boil down to one calculation: "The question that Brits have to ask themselves is values versus their wallets."