Stow says, “King Lud, repairing the city, called it after his name Lud's town; the strong gate which he built in the west part he likewise named Ludgate. In the year 1260 the gate was beautified with images of Lud and other kings. Those images, in the reign of Edward VI., had their heads smitten off .... Queen Mary did set new heads upon their old bodies again. The twenty-eighth of Queen Elizabeth the gate was newly and beautifully built, with images of Lud and others, as before.” (Survey of London.) The more probable etymon of Lud-gate is the Anglo-Saxon leode (people), similar to the Porto del populi of Rome.
[Lud] Built that gate of which his name is hight, By which he lies entombëd solemnly.
Ludgate was originally built by the barons, who entered London, destroyed the Jews' houses, and erected this gate with their ruins. It was used as a free prison in 1373, but soon lost that privilege. A most romantic story is told of Sir Stephen Forster, who was lord mayor in 1454. He had been a prisoner at Ludgate, and begged at the gate, where he was soen by a rich widow, who bought his liberty, took him into her service, and afterwards married him. To commemorate this strange eventful history. Sir Stephen enlarged the prison accommodation, and added a chapel. The old gate was taken down and rebuilt in 1586. The new-built gate was destroyed in the Great Fire of London, and the next gate (used also as a prison for debtors) was pulled down in 1760, the prisoners having been removed to the London Workhouse, and afterwards to the Giltspar Street Compter.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Ludgate from Infoplease: