The Prime Minister laid wreaths at the graves of Private John Parr of the Middlesex Regiment, who died on August 21 1914 - the first UK soldier to be killed in the conflict - and the last to be killed, Private George Ellison of the Royal Irish Lancers, who died on the Western Front on November 11 1918, at 9.30am before the Armistice came into effect at 11am.
At the grave of Private Ellison, in blue pen on a headed Downing Street card attached to the garland of poppies, Mrs May wrote: "They were staunch to the end against odds uncounted ... We will remember them."
In the note left by the resting place of Private Parr, Mrs May quoted a line of wartime poetry - The Soldier written by Rupert Brooke.
She wrote: "There is in that rich earth a richer dust concealed."
The sonnet was written by Brooke, an officer in the Royal Navy, while on leave at Christmas and formed part of a collection of work entitled 1914 which was published in January 1915.
Brooke never experienced front-line combat and died from blood poisoning on April 23 1915 after being bitten by a mosquito while sailing to Gallipoli. He was buried on the island of Skyros.
During the brief visit, she and Mr Michel then met British and Belgian serving members of the armed forces.