The sketch in which Rupert Grint is given a script to give to Daniel Radcliffe was based on an actual event in which Matt Lucas was given a script to give to David Walliams.
Although seemingly an Arab character, Omar Baba is somewhat based on the Greek Cypriot entrepreneur Stelios Haji-Iannou, the founder of budget airline EasyJet. His appearance is similar to Stelios (balding, overweight, unibrow), and one of the jokes satirizes the fact that his shipping-magnate father gave him £30 million to start his business empire. Omar's strategy of cutting corners to provide low-cost flights satirizes the business practices that European budget airlines such as Ryanair have been found guilty of, and the name of his airline FlyLo is a takeoff of Flybe and uses the same font in its logo.
'Come Fly With Me' and 'Little Britain' have many connections to 'Doctor Who.' The narrators of the mentioned shows were Tom Baker, who played the 4th Doctor (1974-81), and Lindsay Duncan, who appeared in the Doctor Who movie 'The Waters of Mars.' Matt Lucas and David Walliams have also both appeared in Doctor Who; Walliams was in 'The God Complex' (2011) and Matt Lucas has a recurring role as Nardole. Also, a character in 'Come Fly with Me' is named 'Penny Carter', also there is a character called Penny Carter in Doctor Who in the episode Partners in Crime (2008)