Terry-Thomas's plane gets stuck between the carriages of a Paris-bound train (in fact filmed on the single-line track between Bedford and Hitchin). Just before the train plus plane goes into a tunnel you can see the cooling towers of Bedford's Goldington Power Station (circa 1960) behind TT's head.
In the beginning of the movie there is a reference to a Frenchman who had crossed the Channel by plane in the previous year (1909). The man meant is Louis Blériot, who flew from Calais to Dover in his famous craft 'Blériot XI' in 37 minutes. Again it was a competition race, for a 1000 Pounds set by the London Daily Mail.