US President Donald Trump has said he believes Britain can have a "very very substantial trade deal" with the US after it leaves the EU.
Mr Trump spoke to business leaders at a meeting co-hosted by the prime minister on the second day of his state visit.
The pair are now meeting for talks, with contentious issues such as doing business with Huawei on the agenda.
Protests are expected across the UK with Labour leader Jeremy Corbyn due to address a rally in London.
Mrs May is also expected to set out the UK's position on climate change and Iran during the meeting with the president at Downing Street.
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The breakfast meeting of five British and five American firms, senior ministers and officials at St James's Palace was held in a bid to boost trade links.
Mr Trump said he believed there was scope for further expansion of trade between the US and the UK.
"I think we will have a very, very substantial trade deal," he told Mrs May.
"This is something you want to do and my folks want to do," he added.
Mrs May said there were "huge opportunities" for Britain and the US to work together in the future.
"It is a great partnership but I think a partnership we can take even further," she told the president, adding: "Of course that is with a good bilateral trade deal."
Thousands of people are expected to join protests against Mr Trump's visit on Tuesday.
A "national demonstration" in London's Trafalgar Square began at 11:00 BST (06:00 Eastern Time), while protests are also planned in Birmingham, Stoke, Sheffield, Glasgow, Edinburgh, Chester, Leicester, Oxford and Exeter.
Organisers have called for a carnival atmosphere, but a huge police operation is taking place in central London to prevent any disruption to Mr Trump's trip.