The men were the siblings of Olive Middleton, Kate’s great-grandmother, who worked as a nurse with the Voluntary Aid Detachment during the war, and was married to Richard Middleton.
When shown an official letter from Buckingham Palace conveying the sympathy of King George V after the third brother had died, the duchess said: “I’m sure so many families had this type of letter and sad stories.”
She also reacted to the brief telegram sent by her great-grandfather Richard Middleton, an Army officer, who wrote to his father-in-law saying Francis’ body had been found after he was killed instantaneously by a bomb during the Battle of the Somme.
Kate said: “It’s so bland, hardly any words.”
The family papers were donated by one of Kate’s distant relatives around a month ago and now form part of the Imperial War Museums’ documents archive.
The duchess toured the popular visitor attraction, which was full of school groups and parents with their children to see the documents and visit the First World War Galleries.
Anthony Richards, head of documents at the institution, said about the telegram: “It’s a very formal sort of brief way to give the family what is essentially terrible news that their loved one has been killed in action.
“You break someone’s heart in just a few words in a telegram.”
He added that Kate had known about the three brothers who fought and died for their country after one of her grandfathers had done some research about the trio.
Mr Richards said: “She was extremely interested in them, it’s always nice to have that family connection that helps you understand something like the First World War.”
During the visit, the duchess also saw a letter written by her great-grand uncle Maurice, the middle brother, to his father Francis Lupton describing life in a dug-out or trench which offered them “a little place you can crawl into for protection from a shell or bullet”.
At the time the note was penned, May 24 1915, the weather was very hot and the wind blew towards the German lines which prevented them “using their gas business”.
The men were allowed to relax in the sun and listened to the occasional shell flying overhead which Maurice thought the enemy fired “through sheer boredom or to satisfy themselves that their guns are still working properly”.
Kate said about the letters written by the brothers: “What really struck me is the positivity, they’re writing home with such a positive light.”
She added: “At the beginning there’s that real enthusiasm.”
Maurice, a captain with the 7th Battalion, West Yorkshire Regiment, described meeting his brother Lionel over the previous days in his letter, but on July 16, 1916, Lionel sent a field service postcard on the day he died.
Printed with phrases like “I have been admitted to hospital” that servicemen had to cross out, Lionel’s note read “I am quite well, I have received your letter, letter follows at the first opportunity.”
A lieutenant, who served with the 28th Brigade Royal Field Artillery, he was the youngest of the three brothers and was killed by a shell, aged 24 in 1916.
The eldest brother Francis, a major serving with the 8th Battalion, West Yorkshire Regiment, was killed by a bomb during the Battle of the Somme in February 1917, aged 31.
Maurice was the first of the siblings to die, killed by sniper fire in 1915 aged 28.
When Kate first arrived at the Imperial War Museums in south London she was shown a striking installation artwork on the outside of the building.
Wearing a Jenny Packham outfit she marvelled at the artificial poppies cascading from the roof by artist Paul Cummins and designer Tom Piper.
And later she was taken on a tour of the First World War Galleries which told the story of the conflict through the uniforms, weapons, documents and equipment of the men who fought.