Blackfriars Station London | Parking, Map and Departures
Blackfriars station is a key transport hub in central London. It consists of two interconnected stations: a mainline railway station and a London Underground station. The Underground station, served by the Circle and District lines, is the older of the two, having opened in 1870. The mainline station came a bit later and offers national rail connections.

Blackfriars stationĀ to Luton Airport
The driving distance from Blackfriars station, London to Luton Airport is 34.8 miles and it should take about 1 hour 12 minutes to get there. See the directions here.
At this time, I am unable to find information on public transport options using Google Maps.