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UPDATE 6-Trump promises UK a "phenomenal" post-Brexit trade deal, solution to Huawei discord

Steve Holland and William James

Huawei discord@

* Trump promises "phenomenal" trade deal

* Trump praises greatest alliance in world

* May says allies can disagree sometimes

* Trump: Brexit will happen and could be good (Recasts with Trump-May news conference)

LONDON, June 4 (Reuters) - U.S. President Donald Trump on Tuesday promised Britain a "phenomenal" post-Brexit trade deal and pledged to work out any differences with London on the role of China's Huawei in building 5G networks.

Feted by Queen Elizabeth on the first day of his state visit to Britain, Trump turned to politics on Tuesday and congratulated outgoing Prime Minister Theresa May and singled out two of her potential successors for praise.

The collapse of May's premiership over Brexit had raised concerns that Trump could publicly humiliate May.

Instead, Trump steered clear of rhetoric that could embarrass her and glossed over even the most sensitive issues such as Huawei and her succession.

Trump mentioned Boris Johnson, who has said the United Kingdom should leave the European Union on Oct. 31, deal or no deal, and Jeremy Hunt, Britain's foreign minister who has warned against leaving without a deal.

"I know Boris, I like him, I've liked him for a long time. I think he would do a very good job," Trump told reporters at a news conference beside May at Britain's Foreign Office.

"I know Jeremy, I think he'd do a very good job," he added.

When asked if an interim decision by British ministers to allow Huawei a limited role in 5G networks would affect security cooperation with Britain's biggest ally, Trump said he would work out the issues.

"We have an incredible intelligence relationship and will be able to work out any differences," Trump said.

"We did discuss it, I see absolutely no limitations, we have never had limitations, this is a truly great ally and partner and we will have no problem with that," he said.

The Trump administration has told allies not to use Huawei's 5G technology and equipment because it fears that would allow China to spy on sensitive communications and data. Huawei denies it is, or could be, a vehicle for Chinese intelligence.

Trump's state visit, promised by May back in January 2017 when she became the first foreign leader to meet him after he took office, has been cast as a chance to celebrate Britain's "special relationship" with the United States, boost trade links and reaffirm security cooperation.

On Brexit, Trump said Britain's EU divorce would happen.

"I would say ... I would think it will happen and it probably should happen. This is a great, great country and it wants its own identity, it wants to have its own borders, it wants to run its own affairs. This is a very, very special place.

"As the UK makes preparations to exit the European Union, the United States is committed to a phenomenal trade deal between the US and the UK," Trump said.

He said he had refused to meet opposition Labour Party leader Jeremy Corbyn, a veteran socialist who criticised Trump at a protest in central London on Tuesday.

Trump said Queen Elizabeth was a "fantastic woman" and thanked Britain for the state visit which he said had cemented the greatest alliance the world had ever known.

May praised the "precious and profound" alliance between the United States and the United Kingdom but said friends could also be open where they disagreed - such as on the Iran nuclear deal and the Paris climate agreement.

(Writing by Guy Faulconbridge; Additional reporting by Elizabeth Piper, Andrew MacAskill, William James, Costas Pitas, Kate Holton, Kylie MacLellan and Michael Holden; Editing by Peter Cooney and Jon Boyle)