The American President had already met Her Majesty, and other senior members of the royal family, at the Eden Project on 11 June where the world leaders were present to discuss the climate crisis and loss of biodiversity around the world.
When Mr Biden travelled to London he was given a Guard of Honour and afternoon tea at the palace, both accompanied by the Queen. He told reporters “she reminded me of my mother, the look of her and just the generosity”.
Despite the praise, Mr Biden has subsequently been accused of potentially breaking royal protocol for numerous infractions, including wearing his sunglasses outside and disclosing the topic of conversation.
On the royal website it says: “There are no obligatory codes of behaviour when meeting The Queen or a member of the [family], but many people wish to observe the traditional forms.”
It then details how to greet the Queen (men bow the head and women curtsy or either can shake hands) and how to address her (Your Majesty and Ma’am on second mention).
It does not include other details about protocol but numerous high profile figures have been accused of breaking it over the years.
Joe Biden met the Queen twice in short succession in mid-June, six months into his Presidency on his first international tour, which began at the G7 summit in Cornwall.
Reports suggested he broke protocol over numerous details including sharing the contents of his conversation with the Queen, telling reporters: "She wanted to know what the two leaders that I - the one I’m about to meet with, Mr Putin, and she wanted to know about Xi Jinping.”
The contents of the Queen’s weekly meetings with the Prime Minister are kept confidential.
Biden’s motorcade also seemed to arrive after the Queen’s at the Eden Project, despite etiquette experts Debrett’s saying that normally everyone should arrive “before the royal personage”.
In 2018 the Vogue editor-in-chief Anna Wintour sat next to the Queen in the front row at London Fashion Week. Wintour, who is renowned for her huge sunglasses, kept them on.
Former royal butler Grant Harrold told the Press Association: "She should have removed them before being in the presence of the Queen, let alone in discussion.
"Eye contact is important while holding a discussion, and not removing sunglasses is the height of bad manners and a serious breach of royal protocol,” he said. "If the Queen gave her permission to keep them on then that would be acceptable, however this would be unlikely."
During his trip to the UK, Trump was also given an audience at Windsor Castle. During an inspection of the Coldstream Guards, within minutes of their meeting, photographs showed Trump walking ahead of the Queen. She then swerved around him.
He also seemed to put a hand on the monarch’s back as she stood for a toast at the state banquet.
In 2019, the palace was reportedly not pleased with former Prime Minister David Cameron, after he spoke publicly about a conversation he’d had with the monarch over the Scottish independence referendum in 2014.
Mr Cameron told the BBC he had asked whether the Queen could "raise an eyebrow", in other words, to show disapproval of the potential plans to leave the union.
The Queen rarely, if ever, comments on politics in her diplomatic life and senior members of the royal family do not vote - something confirmed by Prince Harry after his move to the US when he said he had not voted “in his entire life”.
During a trip to the UK in 2009 with her husband, then President Barack Obama, Michelle was photographed hugging the Queen - certainly not usual protocol for visiting dignitaries.
But fortunately for Ms Obama, the Queen was happy to do so. The Queen’s former dressmaker and close friend, Angela Kelly, wrote in her book: "Much has been made about the meeting between Michelle and Her Majesty when an instant and mutual warmth was shared between these two remarkable women, and protocol was abandoned as they stood closely with their arms around each other’s backs.
“In reality it was a natural instinct for the Queen to show affection and respect for another great woman and really there is no protocol that must be adhered to."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies