Based on the stories by Agatha Christie, a popular and long running series, but to be honest it's a triumph of style over substance. It always looks very good, but has serious problems with chronology.
Episode 02.06: Double Sin
Features preserved Shotters of Brighstone (Isle of Wight) CDL792, a 1939 Bedford WTB with Duple body, seen here with fictional 'Speedy Tours' fleetnames:
Episode 03.01: The Mysterious Affair at Styles
Brief appearance by an LGOC S-type, S454 (XL8962), new in 1922:
There's also this Ford Model TT, DD475:
Episode 03.05: Wasp's Nest
London Transport ST922 (GJ2098), a 1932 AEC Regent/Tilling preserved at Cobham Museum, passes Arnos Grove Underground station, redressed for the show as 'Marble Hill':
Episode 05.02: The Underdog
Has a scene in which Southern National 3560 (YD9533), a 1934 Dennis Ace, conveys a suspect to a nearby railway station. 'Northampton' is the destination (!) - note the fleetnames have been removed, but not the boards advertising 'Forte's Ice Cream Parlour on the Esplanade': (thanks Phil Groocock)
Episode 05.05: The Adventure of the Italian Nobleman
1925 Morris Commercial charabanc YL740 appears in a chase scene. This vehicle is in the Oxford Bus Museum's exhibition devoted to the work of William Morris/Lord Nuffield. (thanks Mike Lloyd):
Episode 05.06: The Chocolate Box:
Carlos Wallberg notes this episode filmed in Brussels: "Some tramways at a station where Poirot drinks a coffee are shown, particularly car 301.". This is of course, actually the Brussels Tramway Museum:
He also notes a bus in yellow/green; this is Autobus Bruxellois 515, with bodywork built by Ragheno in 1946 on a 1939 Brossel AB6DS chassis that had somehow survived the Second World War, which appears in two separate scenes:
Episode 11.03: Third Girl:
Following a woman on a bus can be difficult if she gets off before you've paid your fare. A brief scene aboard 1937-built London Transport STL2377 (EGO426):