Thameslink has a direct and fast service that links Luton Airport railway station with London city center.
Landed at Luton airport, take the shuttle bus at the Stop area 1, which is outside the terminal. It will bring you to the Luton Station in 10 minutes, from where you can take a Thameslink train for London.
In London you can choose to get off at the following stations: Kings Cross/St. Pancras International - Farringdon - City Thameslink - Blackfriars - London Bridge (in zone 1) and East Croydon (zone 5).