Between Paddington and Farringdon. A grand opening on the 9th preceded the opening to the public on Saturday 10 January 1863.
“That afternoon Hetta trusted herself all alone to the mysteries of the Marylebone underground railway, and emerged with accuracy at King’s Cross. She had studied her geography, and she walked from thence to Islington.” This description of an early underground journey, by a woman alone, comes from the 1875 ‘The Way We Live Now’ by Anthony Trollope (p.385 in vol.2, Penguin 2001). Living in Welbeck Street Hetta probably got on at (Great) Portland Street.
See Metropolitan Railway Company for more information.
It's interesting that, in 1829, George Shillibeer had launched the first omnibus service on a quite similar route: Marylebone Road to the Bank. Both services were catering to the middle classes who lived to the west and worked in the City.