Theresa May has emphasised the importance of Nato and the European Union for security and said she is "confident" of striking a trade deal with the United States despite Donald Trump's "America first" strategy.
The Prime Minister moved to deal with concerns about the new president's apparently nationalist approach and said she would hold "very frank" talks with him when she visits Washington DC.
Officially Mrs May is expected to visit the controversial commander-in-chief in the spring and a Number 10 source has dismissed as "speculation" reports that she will travel to the US as soon as next week.
In his inaugural address, Mr Trump sparked concerns in Britain about the prospect of reaching a quick free trade agreement with the US to offset any Brexit-related economic hit.
The president promised that "every decision on trade... will be made to benefit American workers and American families" and Labour MPs were swift to question what it meant for the UK.
But in an interview with the Financial Times, Mrs May said: "I'm confident we can look at areas even in advance of being able to sign a formal trade deal.
"Perhaps we could look at barriers to trade at the moment and remove some of those barriers to open up that new trading relationship."
On a visit to Burma, Foreign Secretary Boris Johnson backed the PM, saying he was "very optimistic" about striking a trade deal but insisting "it's got to work for the UK as well".
"I think that the new president has made it very clear that he wants to put Britain at the front of the line for a new trade deal and obviously that's extremely exciting and important," he told reporters.
On Friday, Mr Trump again provoked worries about his commitment to Nato at a time when Russia is showing increasing aggression.
The president complained that the US had "subsidised the armies of other countries" and "defended other nations' borders while refusing to defend our own".
Baltic nations, which fear Russian incursion as Vladimir Putin masses troops on their borders, will hope Mr Trump was simply urging other Nato members to boost their defence spending rather than signalling a desire to leave the alliance of mutual protection.
Mrs May said she was sure the new president "recognises the importance and significance of Nato".
The PM also moved to emphasise the value of the EU for collective defence and security, following Mr Trump's suggestion in an interview earlier this week that he would welcome the break-up of the union.
The president described the EU as a "vehicle for Germany" and predicted "others will leave".
But Mrs May said: "I'm also confident the USA will recognise the importance of the co-operation we have in Europe to ensure our collective defence and collective security."
Addressing accusations of racism and misogyny against Mr Trump, Mrs May made clear she found some of his comments "unacceptable", including his suggestion that his fame allowed him to "do anything" to women, such as "grabbing them by the pussy".
As tens of thousands of protesters prepared to join women's marches against the Trump presidency in London and around the world, Mrs May said: "The whole point about a (special relationship) with the US is that we can sit down and be very frank with each other about what we think."
The PM distanced herself from suggestions she and Mr Trump could mirror the Reagan-Thatcher relationship of the 1980s, saying she does not want to "emulate" models from the past but stressing she is confident they can have a "very special relationship".
Britain's former ambassador to Germany said concerns over Mr Trump's stance on Nato could lead Berlin to take a much tougher stance in Brexit negotiations to preserve the unity of EU and the security it provides.
Sir Peter Torry told BBC Radio 4's Today programme: "I think the lessons here are for us in the UK, for Brexit, because the more that it turns out to be the case, which hopefully it won't be, but the more it turns out to be the case that the Americans move away from the security guarantees incorporated by Nato, the more the Germans are going to be anxious to preserve the unity of the EU.
"In the same way as we're prepared to pay any political cost virtually to regain control over our borders, the Germans are going to pay any economic cost to retain the unity of the EU and that means I think quite hard-nosed negotiations."