There are two possible answers to this question as there are two companies competing for the title.
Also, by answering this question we can also answer some others along the way. If we can work out which railway came first we can work out which is London's oldest station, too.
The Surrey Iron Railway
The first Act of Parliament for the authorisation of a railway in the London area was granted in 1801, to the Surrey Iron Railway. This railway was built in stages, between 1802 and 1803, from Frying Pan Creek, on the River Thames at Wandsworth, to Pitlake Meadows at Croydon, mostly following the Wandle Valley.
The Surrey Iron Railway used trains of ten wagons, which were horse-drawn along a narrow-gauge, double-tracked line. This line remained in use until 1846, but was only briefly profitable.
However, all of this railway was within Surrey, parts of which wouldn't become part of London until 1889.
The London and Greenwich Railway
In 1831, following the success of the Liverpool and Manchester Railway, which had opened in 1830 as the world's first passenger railway to connect two cities, retired Royal Engineer Colonel George Thomas Landmann and George Walter, an entrepreneur, had the idea for a passenger railway service in London.
