Thameslink operates a train from Luton to Shoreditch every 15 minutes. Tickets cost $16 - $23 and the journey takes 46 min. Alternatively, Green Line (operated by Arriva) operates a bus from Luton to Shoreditch every 30 minutes. Tickets cost $13 and the journey takes 1 h 12 min.
From Luton train to Blackfriars then line 388 bus to Shoreditch, Bethnal Grn Rd Shoreditch High St. 1 h 5 min £16. From Luton Station Interchange (Luton Railway Station) bus to Baker Street Station then line 205 bus to Shoreditch, Great Eastern Street. 1 h 48 min £11. From Luton taxi to Shoreditch. 47 min £150. From Luton drive to Shoreditch. 47 min £6.