It will hang in the RAF Club and the Queen watched her portrait being unveiled when she visited the institution in London’s Piccadilly to celebrate its 100th anniversary.
Mr Sullivan, who won the BP Portrait Award in 2017, chatted to the Queen whose visit was her first official engagement of the autumn outside Buckingham Palace.
He said about his sitting with the Queen at Windsor Castle: “I was saying it was quite cold when we did it because it was the end of February and she said, ‘it doesn’t look like I’m cold’ so I think by then we had some extra heaters brought up.
“I think the idea was to capture something of the role of the monarch, but one tries to get behind that to the person.
“And I really like the idea her handbag was placed in front of the gilt chair. It was almost happenstance that it was placed there but it gives some idea there’s actually a person as well as a figurehead – it’s personal.
“It’s where she put it, and I thought I could take it out, but then I thought – actually it’s quite a nice thing, a personal thing.”
During the visit, the Queen opened a new wing at the club, home to a fitness suite and business centre, and a newly commissioned stained glass window designed to commemorate women in the Royal Air Force.
The artwork was created by stained glass artist and designer Helen Whittaker, and highlights the development of female roles in the RAF by featuring parts of planes, vehicles and other equipment they have used over the decades.
Jo Salter, Britain’s first female RAF fast-jet pilot, and Christine Ryan, 76, who was a member of the Women’s Royal Air Force in the 1960s, talked the Queen through the window’s main elements.
The artwork featured large glass “rivets”, which when looked through showed a picture of women performing roles in the RAF, and the Queen was directed towards one that told the story of Noor Khan.
A campaign is building to have an image of Khan, who joined the WAAF (Women’s Auxiliary Air Force) during the Second World War and later became an agent with the Special Operations Executive, featured on the £50 note.
The agent, who was of Indian and American descent, was the first female radio operator to be sent into France, but was later executed by the Gestapo and posthumously awarded the George Cross.
When a Crossley tender steering wheel was pointed out to the Queen – symbolising the women who drove the military vehicle during the First World War – Mrs Ryan mentioned the monarch’s wartime role with the Auxiliary Territorial Service (ATS) as a driver.
The Queen spent a period in uniform, joining the ATS in February 1945 at the age of 18.
By the end of the Second World War she had reached the rank of junior commander, having completed her course at No 1 Mechanical Training Centre of the ATS and passed out as a fully qualified driver.
Later Whittaker, who helped create David Hockney’s Westminster Abbey stained glass window for the monarch, said she had asked the Queen about her time with the ATS when they met, adding: “It felt like she was thinking back, she did a wry smile – a little grin.”
The RAF Club is where the Duke of Edinburgh was caught on camera apparently swearing at a photographer during a photocall with Battle of Britain veterans in 2015.
The incident happened on the day the Queen and other members of the royal family joined the former military fliers – famously dubbed the “few” by wartime leader Winston Churchill – to mark the 75th anniversary of the aerial conflict.
Before leaving, the Queen met 101-year-old Jack Lyon, a former RAF flight lieutenant from Bexhill-on-Sea who flew in Whitley bombers as a navigator.