besides the Underground (aka Tube), London has the Thameslink service which is part of the national rail network and links Bedford in the north and Brighton in the south. This link started in 1988 by re-opening the Snow Hill Tunnel around Holborn. This tunnel hadn't carried passenger services since World War I but carried freight until 1970.
Here at Farringdon, construction works are well advanced for Crossrail which is due to open in 2017. This is an east west line, again part of the national rail network with services starting in Reading to the west to Shenfield in Essex in the east with a brand new tunnel section through London's West End and The City.