The Metropolitan Line was the first line but has sections of overground running.
The first deep level tube that still runs in (more or less!) its original format is a section of line that is now part of the Northern Line.
Over the years the track sections have changed hands a number of times and different sections have operated under one or more line names so it is not always easy to define the 'first' of any of the Underground's achievements.
The Central Line
The oldest tube line in London is the Metropolitan Line, which opened on January 10, 1863. It was the first underground railway in the world and initially ran between Paddington and Farringdon. The line was designed to alleviate congestion on the streets of London and has since expanded significantly.
The Northern Line.
The London Tube, the first underground railway system in the world, was built in the mid-19th century. The first line, the Metropolitan Railway, opened in 1863.
The Circle Line.
District Line (London Underground) from Hammersmith tube station to Victoria tube station.
Camden
Camden
The Central line is the current oldest tube stock in the whole of the London Underground.
The Circle Line Unfortunately this answer is wrong! According to Transport for London the only tube line to connect all London Underground lines is the Jubilee Line.
The Tube lines in London, in order, are: Bakerloo Line, Central Line, Circle Line, District Line, Hammersmith & City Line, Jubilee Line, Metropolitan Line, Northern Line, Piccadilly Line, Victoria Line, and Waterloo & City Line. Each line is color-coded on the Tube map and serves various areas of London, connecting key stations and landmarks.
Depends on the context: London has a tube (Metro) line which is called the Circle Line.