According to the Second Doctor, the Battle of Trafalgar was the most important English victory by sea in the Napoleonic Wars. On 21 October 1805, the Royal Navy, led by Lord Admiral Horatio Nelson, defeated a French and Spanish fleet. However, Nelson was killed in the fighting. (PROSE: World Game)
Prior to the battle, the Player known as the Countess attempted to ensure Napoleon's victory by helping Fulton develop a prototype submarine, known as the Nautilus. With the machine limited in its ability to move underwater with the technologies at hand, the Countess had attempted to enhance its power by providing Fulton with an omega drive, but the Second Doctor was able to sabotage the drive and convince Fulton and Napoleon to abandon the plan (PROSE: World Game).
The Eleventh Doctor and Amy Pond visited a different ship during the battle. It was fleeing from what they believed to be a Kraken. It was actually a 21st century aircraft carrier brought back in time by an infestation of Time Roaches. The Doctor sent it back into the Time Vortex, causing the carrier to return to its own time. (COMIC: Rough Waters)
After hunting the Flying Dutchman through time, the Twelfth Doctor, Prince George, and Thorpe finally boarded it at the battle of Trafalgar. They materialised on a French ship and were shot at by a French soldier. They jumped off the ship and landed on the Dutchman. While they were on the Dutchman it left 1805. After the Doctor took control of the ship, he took it back to the battle and retrieved his TARDIS. (COMIC: Ghosts of the Seas)
After the English won the battle, Nelson was shot down by a sniper. (PROSE: World Game) The Second Doctor, Ben Jackson and Polly Wright visited Nelson's ship during the battle. The Doctor tried to change history by preventing Nelson's death, but was unsuccessful. (PROSE: H.M.S. TARDIS)
Sometime before his eighth incarnation, the Doctor told Iris Wildthyme that he was instrumental at Trafalgar. (PROSE: The Scarlet Empress) The Doctor later told Izzy Sinclair that he used a sextant to calculate the position of Napoleon's fleet at Trafalgar. (COMIC: Fire and Brimstone)
The First Doctor's companion Vicki Pallister, a native of the 25th century, was unfamiliar with history of the battle and that of Trafalgar Square. On a visit to London in November 1605, she expressed an interest in visiting the square. When the Doctor told her that the Battle of Trafalgar would not occur for another 200 years, she assumed that he meant that a battle had been fought in Trafalgar Square in 1805. (PROSE: The Plotters)