May also said she was optimistic about hoped-for future trade pacts with the US and other countries after meeting Trump at the Group of 20 summit.
Trump said a deal between the US and Britain, which is leaving the European Union, would be "great for both countries" and can be achieved quickly.
Trump also squashed speculation that he would not be visiting London after all, saying that "we'll work that out" and he will be making the trip.
But opposition to the idea mounted quickly. Some Britons called the invitation premature given the divisiveness of the US presidential race and Trump's political inexperience. Last month, London's mayor called for the invitation to be rescinded after Trump criticized the mayor's response to a deadly extremist attack.
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May said Trump made clear "that he was very keen to come to London." She said she looked forward to welcoming him and "we are working on what a suitable date would be for such a visit."
"We're working on a trade deal, which will be a very big deal, and a very powerful deal, great for both countries," he said as he met May in Hamburg. "And I think we'll have that done very, very quickly.