Tens of thousands crammed central London’s streets. The roar of cheers was as deafening as the flypast. “We want Wilson,” chanted the crowd, packed tightly beneath a “brilliant mass of flags” stretching from Charing Cross to Buckingham Palace, the Guardian reported at the time.

In 100 years of US presidential visits, since Woodrow Wilson became the first Oval Office incumbent to visit the UK , the so-called “special relationship” has waxed and waned. And the warmth of Britain’s welcome has served as a telling gauge.

Wilson – carriage-borne in postwar jubilation along a Mall lined by 20,000 soldiers, their “bayonets bright in the December sunshine” – arrived on Boxing Day 1918 for his two-day visit and would be feted in London, Manchester and Carlisle.

One century on, and Donald Trump would also attract tens of thousand to the streets; a seething crowd united in protest beneath a huge orange baby blimp.

The Donald Trump baby balloon flies over Parliament Square during a protest in London in July 2018. Photograph: Andy Rain/EPA

Tucked away – official dinner at Blenheim Palace, tea with the Queen at Windsor Castle, and a round at his Turnberry golf course in south Ayrshire – his three-day itinerary in July 2018 was designed to shield him from the protests. Not since the visit of George W Bush had an American president been so unwelcome by the British public.

“Now, compared [with] Trump, ‘Dubya’ seems like Lincoln. It’s remarkable how perspectives change over these people,” said Dr Martin Farr, senior lecturer in modern and contemporary British history at Newcastle University.

Twelve serving presidents have visited the UK since Wilson’s 1918 visit. He arrived at the end of the first world war, ahead of the Paris peace conference, but it would take the second world war to entice another president across the Atlantic. Harry S Truman popped onboard the battlecruiser HMS Renown off Portsmouth for a hurried lunch with King George VI on his way back from the Potsdam conference.

The former supreme commander of the allied expeditionary forces, Dwight – later President – Eisenhower, came in August 1959 and was the first serving president to be received by the Queen. The warmth of their relationship was reflected in a handwritten note she sent afterwards. “Seeing a picture of you in today’s newspaper standing in front of a barbecue grilling quail reminded me that I had never sent you the recipe for the drop scones which I promised you at Balmoral. I now hasten to do so,” she wrote.

Woodrow Wilson and King George V leaving Buckingham Palace in a carriage in about 1920. Photograph: Fox Photos/Getty Images

For John F Kennedy’s arrival in 1961, half a million people reportedly lined the route between the airport and the West End in London. He and his first lady, Jackie Kennedy, were political showbiz. Colour footage captured the couple’s youth, glamour and charisma. He visited again in 1963, calling on Harold Macmillan. “This was a time of the cold war, heightened tensions between east and west, the missile crisis, Bay of Pigs … and the leader of the free world looks up to our prime minister,” said Farr of Britain’s response.

Sometimes it was the lack of a visit that spoke loudest. Lyndon Johnson never came, furious at Harold Wilson’s refusal to send him so much as a marching band in support over Vietnam. Perhaps the warmest welcome was extended to Jimmy Carter, who endeared himself in 1977 despite rashly kissing the Queen Mother smack on the lips. “I took a sharp step backwards, but not quite far enough,” she later commented.

Carter, a Dylan Thomas fan, had hoped to be able to visit south Wales during his trip. Labour’s Jim Callaghan, his party facing a byelection in the north-east, had other ideas and whipped his guest up to Tyneside.

“Carter was told in the car by the local MP, ‘If you say Howay the lads everyone will love it,” said Farr. On the podium outside Newcastle’s Civic Centre, Carter leaned into the microphone. “Howay the lads,” he bellowed as crowd erupted. “I’m grateful to be a Geordie now,” added the peanut farmer from Georgia.

The Queen, welcomed by Dwight Eisenhower in Washington on 18 October 1957, would return the courtesy two years later. Photograph: AFP/Getty Images

“They packed the airport. They packed the streets. They packed the area outside the Civic Centre and they opened their arms to him,” reported the local newspaper, the Chronicle.

“Even though it’s 40 years ago, it is still striking,” said Farr. “Our narrative now is that these were two failed leaders.” But the visit was the warmest, and perhaps happiest.

Ronald Reagan and his wife Nancy were greeted by 115,000 anti-nuclear war protesters gathered in Hyde Park. The welcome for George W Bush in 2003, in the immediate aftermath of the overthrow of the Iraqi dictator Saddam Hussein, was even chillier.

With the then prime minister Tony Blair vowing to “stand firm” with America over Iraq, thousands of anti-war protesters assembled in cities across the UK, waving placards and wearing T-shirts with the slogans “Stop the War” and “It’s about the oil, George”. A well-aimed egg was lobbed at the presidential motorcade, and a Bush effigy “toppled” in Trafalgar Square, as 67 were arrested.

“One curiosity is that it’s always Democrat presidents that are popular,” said Farr, currently editing a book on presidents and premiers. “There’s a curious mapping of popular sentiment which is clearly supportive of more liberal presidents.”

With Barack Obama, “everyone wanted to be part of it. He was a phenomenon, really,” added Farr. It was difficult to get any MP to criticise his state visit, during which he addressed both Houses of Parliament.

“You have genuine charm. Obama thought the Queen and Duke of Edinburgh are wonderful, and told the world he adored them. That went down very well with the British press. So, a bit of gumption goes a long way.”

What appears to have united all of these visits was convention, Farr believes. Even when there were Anglo-American disagreements, there was at least diplomatic language and due process, he said.

That is, until Trump, who insulted Theresa May in a Sun interview, saying her Brexit policy would “probably kill” a US-UK trade deal, and then praised Boris Johnson as likely to “make a great prime minister”.

• This article was amended on 26 December 2018. An earlier version described the British battlecruiser HMS Renown as a yacht.