Trafalgar Square was a large square in the middle of London. According to the Fourth Doctor, "a good protest always ends up in Trafalgar Square." (AUDIO: Energy of the Daleks) It consisted of Nelson's Column and three lion statues. There was also a fourth, empty plinth; in the 21st century, arts were periodically shown off there. (PROSE: Magic of the Angels) Harry Sullivan, upon experiencing his first voyage in the TARDIS, noted that the ship would be incredibly useful in Trafalgar Square, "hundreds of bobbies hiding inside it." (TV: The Ark in Space)
On a visit to London in November 1605, the First Doctor's companion Vicki Pallister, a native of the 25th century, 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)
On 23 October 1843, the Fifth Doctor, Nyssa and Tegan Jovanka visited the square, which Tegan claimed was more "tourist friendly" in 1982. The Doctor climbed Nelson's Column and found its builders Samuel Morton Peto and Thomas Grissell had been taken over by two Sevakrill. In addition, they had installed a missile inside the column which was faced downwards, ready to destroy the Earth in 2017. This would distract the Charnal horde, enemies of the Sevakrill, allowing them to gain a strategic advantage.
To protect this operation, they installed several stone lions, made invisible by perception filters. These lions began chasing Nyssa and Tegan. In the process, they killed seven civilians and a policeman. The Doctor managed to appeal to Peto and Grissell and they broke free. The lions returned to their plinths and the Doctor hoped that, when their perception filters wore off in a few decades, Sir Edwin Landseer would unveil them as his own creation, as was the case. The Doctor then spent two weeks lowering the missile into a shaft beneath column and building a floor to cover it. By this time it was November, and the statue of Nelson was being added when the Doctor departed. He left behind a short range sensor in the square to warn him if the Sevakrill ever tried to reactivate the missile. (PROSE: The Lions of Trafalgar)
On 8 May 1945, a party was held in Trafalgar Square to celebrate VE Day. (PROSE: Magic of the Angels) The Seventh Doctor and his companions Ace and Hex were present in London for the celebrations. Prior to this visit, Hex had never heard of VE Day. (AUDIO: Casualties of War)
In 1976, the Seventh Doctor arrived in the square with Ace and Bernice Summerfield, disguising his TARDIS as Nelson's Column by materialising around the actual monument. The Monk caused the TARDIS to take on the form of the Statue of Liberty. (PROSE: No Future)
The Tenth Doctor pulled the interstellar cruise ship Titanic out of a nosedive, narrowly avoiding Buckingham Palace and piloted her along the Mall toward Trafalgar Square, on the morning of 25 December 2008. (TV: Voyage of the Damned)
In 2012, the Eleventh Doctor put two quantum-locked Weeping Angels on the fourth plinth, under the title of "Monument to the Missing" in memory of the Angel's victims, where the two Angels would be in someone's line of vision for many years to come. (PROSE: Magic of the Angels)
In 2014, (COMIC: The Fractures) a forest grew overnight to protect Earth from a massive solar flare. During a school trip, the Coal Hill student Maebh Arden got lost in the brand new woods and was to be found in Trafalgar Square by her teachers and the Twelfth Doctor. (TV: In the Forest of the Night)
During the Dalek occupation of Earth in the 2160s, the Daleks patrolled the square. Barbara Wright and Jenny managed to avoid the Daleks while rolling Dortmun in his wheelchair in their trek across Westminster to Wembley. (TV: The Dalek Invasion of Earth)
While he was busy repairing a circle of transmat refractors on Earth, the Fourth Doctor pointed out to Sarah Jane Smith and Harry Sullivan that Trafalgar Square "should be that way", if the desolate part of Earth they had transmatted to was Piccadilly ten thousand years into Sarah and Harry's future. He told Sarah to "mind the traffic." (TV: The Sontaran Experiment)
The Eleventh Doctor and Amy Pond arrived in the Square in 1963 to learn that the Daleks had invaded Earth. The Daleks were chasing the last human through the square. The timeline was restored when the TARDIS crew travelled to Skaro to destroy the Eye of Time. (GAME: City of the Daleks)
Behind the scenes
In the ultimately unproduced film The Dark Dimension, the Daleks were to have been among several alien races which simultaneously invade London, with one particular scene depicting them gliding round the lions at Trafalgar Square.