Yes. According to National Rail Enquiries it is the Brighton-Bedford Thameslink Service calling at Burgess Hill, Wivelsfield, Haywards Heath, Balcombe, Three Bridges, Gatwick Airport, East Croydon, London Bridge , London Blackfriars, City Thameslink, Farringdon, St Pancras, West Hampstead, St Albans, Harpenden, Luton Airport Parkway, Luton, Leagrave, Harlington, Flitwick and Bedford.
Return trains on this Thameslink route leave London Bridge at 3:35, 4:05, 4:35, 5:05, and 5:35