They had built a missile inside the column and planned to detonate it in 2017, destroying the Earth and distracting the Charnal horde, whom they were at war with. To protect this operation, they had several stone lions, hidden by perception filters, patrol the area. The Doctor managed to appeal to Peto and Grissell and they broke free.
The Doctor 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. (PROSE: The Lions of Trafalgar)
In a timeline where the Daleks exterminated humanity in 1963, Nelson's Column, along with London and presumably the rest of the world, was in ruins. When the Eleventh Doctor and Amy Pond arrived in the Square in 1963, the Doctor's TARDIS landed next to the statues toppled head. The timeline was restored when the TARDIS crew travelled to Skaro to destroy the Eye of Time. (GAME: City of the Daleks)
The Seventh Doctor materialised his TARDIS around Nelson's Column in 1976, The Monk caused the Doctor's TARDIS to change its appearance from that of the column to that of the Statue of Liberty. (PROSE: No Future)