Accompanied by their spouses, the two leaders approached. But just as the prime minister looked like she was about to offer her hand, the US president’s remained firmly by his side.
May and her husband Philip shook hands with First Lady Melania Trump, while the president only shook hands with Philip.
But during a press conference shortly after, Trump and May presented a united stance. May said the special relationship had endured through her premiership, including during the Russian chemical weapon attack in Salisbury.
She added: “I’ve always believed that cooperation and compromise are the basis of strong alliances and nowhere is this more true than in the special relationship.”
In return, President Trump promised a “phenomenal” trade deal following Brexit, adding: “There is tremendous potential in that trade deal, I say probably two and even three times what we’re doing right now.”
But in comments which will be met with stiff resistance in the UK, he added: “I think everything with a trade deal is on the table.
“When you’re dealing with trade, everything is on the table, so NHS or anything else, a lot more than that, but everything will be on the table absolutely.”
Matt Hancock, Secretary of State for Health, had something to say about that.
And on Jeremy Corbyn, Trump was scathing, describing him as a “somewhat negative force” and claiming he turned down a request from the Labour leader to meet.
Trump’s handshakes have already made headlines during his three-day state visit to the UK. The president was involved in what looked almost like a fist bump greeting with the Queen on Monday.
Trump told May earlier today she should “stick around” to secure US-UK trade deal.
May is due to step down as Tory leader on Friday, and as prime minister in mid-July once her replacement is chosen by the party.
The president and prime minister are due to hold a joint press conference later today.
Trump has also offered to hold private talks with Tory leadership hopeful Michael Gove. It has also been suggested he could meet with frontrunner Boris Johnson.
Thousands of protesters were expected in central London to demonstrate against the president and Jeremy Corbyn is due to to address the protest “in solidarity with those he’s attacked in America, around the world and in our own country”.
Elsewhere, the Trump baby blimp has ascended once again over the skies of central London, flying over Westminster after its takeoff from Parliament Square this morning.
Last year it accompanied around 100,000 people in London protesting Trump’s visit. Trump himself said once he laid eyes on it: “I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London.”