From the Wikipedia page 
Ludgate Hill railway station was a station in the City of London opened by the London, Chatham and Dover Railway (LC&DR) as its City terminus on 1 June 1865. It was on the Ludgate (railway) Viaduct between Queen Victoria Street and Ludgate Hill, slightly north of Blackfriars Station.
North of the station Ludgate Viaduct continued to the Snow Hill tunnel to connect with the then recently opened Metropolitan Railway south of Farringdon to enable main-line trains to run between north and south London.
Passenger services through the tunnel ended in 1916, after which services north of Ludgate Hill station ran only the few hundred yards to Holborn Viaduct station which opened in 1874. Ludgate Hill was little used because Holborn Viaduct and Blackfriars stations were close and it was closed on 3 March 1929.
In the 1970s, in the Fleet line proposal, preparatory work began for Ludgate Circus tube station very near the site of Ludgate Hill station, but it was abandoned when a different alignment was chosen for the Jubilee Line, as it later became.
In 1990 the remaining station structures and the Ludgate Viaduct and Holborn Viaduct station were demolished. An office building now stands at the station site, above a new tunnel which connects the old Snow Hill tunnel and Blackfriars station for Thameslink services. City Thameslink station in the new tunnel has a southern exit at Ludgate Circus, roughly on the site of the old Ludgate Hill station.