US President Donald Trump said the US and UK have the "greatest alliance the world has ever known" in a news conference with Theresa May.
The prime minister said they had a "great relationship" that they should "build on".
But they also "openly" discussed their differences, such as on climate change, Iran and China, Mrs May said.
Mr Trump also said he turned down a meeting with Jeremy Corbyn, who addressed protesters in Westminster.
The US president is meeting Brexit Party leader Nigel Farage at the US ambassador's residence, Winfield House.
The Labour leader had proposed talks with Mr Trump, saying he was ready to engage with the US president on issues such as climate change, threats to peace and the refugee crisis.
"I want to be able to have that dialogue to bring about the better and more peaceful world that we all want to live in," Mr Corbyn told the crowd of protesters.
When asked about Mr Corbyn, the US president said he did "not know him, never met him, never spoke to him", adding: "He wanted to meet today or tomorrow and I decided I would not do that."
Effusive Trump promises Britain a "phenomenal" post-Brexit trade deal.
U.S. President Donald Trump on Tuesday promised Britain a “phenomenal” post-Brexit trade deal, dismissed differences over China’s Huawei and glossed over other disagreements as he heaped praise on the United States’ closest ally.