Theresa May also believes she is able to endear the US President into backing NATO, the UN and even the EU.
Speaking to reporters on her flight to the US, ahead of a well-received speech to leading Republicans in Philadelphia, Mrs May said President Trump shared some of her political values, and that of Brexit Britain.
She said: “I think we both share a desire to ensure that governments work for everyone and particularly that governments are working for ordinary working class families.
“I think that’s important. That’s what I’ve spoken about.
“I did it on steps of Downing Street when I became Prime Minister; a country that works for everyone and an economy that works for everyone.
“I think we share that interest and that intention in both our countries.”
Asked ahead of her White House meeting on Friday about the contrast between a vicar’s daughter and a reality TV star, Mrs May joked: “Have you ever noticed that sometimes opposites attract?”
The PM is the first foreign leader to visit the Trump White House and said she was pleased to be going “so early” in the administration.
Mrs May declined to criticise the President’s crackdown on immigration.
She said: “The rules that the US introduces are rules for the US.”
She would not be drawn on his controversial claims about millions of illegal voters.
“What happens in US elections is not a matter for the British PM. It is a matter for US and US authorities,” she said.
The PM also signalled a significant toughening on the language around Iran’s nuclear deal, signed in 2015. Mr Trump has suggested scrapping it.
Mrs May said: “I think it was an important deal that was done and I think it is important that we ensure that the deal is properly enforced.”
Mr Trump said in a speech to leading Republicans that he would be doing the negotiating with the UK.
He said: “I’m meeting with the Prime Minister tomorrow, as you know, of Great Britain… I don’t have my commerce secretary and they want to talk trade… so I’ll have to handle it myself, which is okay.”
During the speech he set out the US approach to trade deals: “Believe me, we’re going to have a lot of trade deals. They’ll be one-on-one. They won’t be a whole big mash pot.
“And if that particular country doesn’t treat us fairly we send them a 30-day termination… notice of termination. And then they’ll come and say please don’t do that and we’ll negotiate a better deal during that 30-day period.”
Some Conservative MPs have warned Mrs May against getting too close to the controversial property tycoon.
Conservative chair of the Commons Health Committee Dr Sarah Wollaston today went public with her criticism.
The PM said: “Donald Trump was elected president of the USA. The UK and US have shared interests and shared challenges we can work together to deal with.
“We have a special relationship. It’s a longstanding relationship. It’s existed through many different PMs and Presidents.
“I believe there is a shared role for UK and US Working together; we can stand up for shared interests and shared values.”