Arthur Wellesley was usually known by his title, the Duke of Wellington. He first met the Second Doctor when the Doctor and his friend Serena thwarted an attempt by the mysterious Players to blow up Wellesley and Lord Nelson at the same time. The two humans were awaiting an appointment with the Prime Minister at 10 Downing Street. After this, the three met again during a ball that took place before the Battle of Waterloo. Serena sacrificed herself to save Wellesley from an assassin.
During the subsequent battle against Napoléon Bonaparte, the Doctor played a vital role in carrying messages through the battlefield. He posed as Napoleon himself, exploiting the superficial similarity between himself and the Emperor. After the battle, Wellesley remarked to the Doctor that "the only thing sadder than a battle lost, is a battle won" (PDA: World Game). The Fourth Doctor later considered how right he was: the only thing harder than losing is winning and realising whom you had lost to reach that point. (EDA: The Eight Doctors) Wellesley fought alongside Oliver Blazington at the battle. (NSA: The Eye of the Jungle)
During a brief visit to 1816, the Doctor met with Wellesley again and took a trip to Brighton with him. They met the Prince Regent, who convinced the Doctor to invest some money he had recently won gambling in a bank that a friend of his had just founded. (PDA: World Game)
In a history project for school, Clyde Langer and Luke Smith were required to show the battle strategies of Wellington and Napoleon at the Battle of Waterloo, while playing a game of Waterloo on Mr Smith. Luke, impersonating Napoleon, referred to Clyde as "monsieur Duke". (SJA: The Last Sontaran)
In the years after the Napoleonic Wars, Wellesley served as British Prime Minister. In 1851, when he was an elderly man near the end of his life, he met the Eighth Doctor's companion Charley Pollard at the Great Exhibition in London. He took an immediate liking to Charley, who was initially unaware of his identity. He permitted her to call him by his first name over the objections of his assistant, Mr Fazackerly. (BFA: Other Lives)