It looks like, to paraphrase [Pete and Dud] (https://en.wikipedia.org/wiki/One_Leg_Too_Few), the film has One Wheel Too Few. From the Imperial War Museum's [The Polish Pilots Who Flew In The Battle Of Britain] (http://www.iwm.org.uk/history/the-polish-pilots-who-flew-in-the-battle-of-britain):

"Pilots of Nos. 302 and 303 Squadrons were ordered to ride tricycles - all equipped with radio, speed indicators and compasses - around airfields in flying formations. The Poles, combat experienced and eager to fight, did not take that kind of approach very lightly. Pilot Officer Jan Zumbach wrote in his memoirs: 'The British wasting so much of our time with their childish exercises, when all of us had already won their wings'."

The main purpose of the tricycles was for training in radio controlled interceptions, where a ground-based controller would direct friendly fighter pilots towards potential targets. There's a section about it in some [Chapters taken from "A First Class Group – The 1939-45 war experiences of S/Ldr W.G. Curtin O.B.E(Mil’y) in 11 Group and 83 Group RAF Operations rooms" (by Simon M. Curtin)] (http://www.americanairmuseum.com/sites/default/files/media/media-16691.pdf), and the Fleet Air Arm adopted the same technique at RNAS Yeovilton in 1941 as related rather well by Mike Crosley in his autobiography They Gave Me A Spitfire:

"One Monday morning, I came back from a weekend at home and found a whole lot of Wall's Ice Cream tricycles - 'Stop-me-and-buy-one's - on the grass outside Air Traffic Control. [...] The Wall's ice cream tricycles were the 'aircraft'. The 'pilots' pedalled them under radio directions from a small transmitter in the Control Tower, which was the 'aircraft-carrier'. Some tricycles were enemy 'bombers'. They pedalled slowly. Others were 'fighters'. They pedalled faster - but only a little faster, we noticed.

The pilots of the bombers and fighters carried their wireless sets where ice cream should have been. The bombers steered a course for the carrier, and the fighters were sent to intercept them. They steered whatever course and speed that Lt/Cdr Coke ordained, using a compass below the handlebars to give them the required direction and a metronome on top of the ice cream compartment to give them their pedalling airspeed.

Neither bomber nor fighter could see where they were going, so we watched each collision as it occurred. We would then listen to the polite comments of the fighter pilot towards the bomber as they unseated each other in mock combat. Sometimes there were r/t failures. The Tower then lost contact, and aircraft would get lost on the airfield and sometimes be seen pedalling slowly down the roads between the hangars or by the Captain's office. We suspected that they had purposely switched off and were making a beeline for the wardroom bar."

Crosley always refers to a fighter controller as a "Stop Me And Buy One" after that, and the description tallies fairly well with the scene from the film, allowing for a little cinematic license; visually it should perhaps look a little more like [this photograph of a pair of WRENs conducting such an exercise] (http://ethw.org/File:17._WRENS_on_Trikes_72.jpg), Dark Blue World may be borrowing from the [31st August 1942 edition of LIFE magazine] (https://books.google.co.uk/books?id=iU4EAAAAMBAJ&printsec=frontcover). Starting on page 88 there's a brief story about air cadets of the 285th Air Training Corps Squadron riding their bicycle 'Spitfires' complete with wooden 'wings'. The pictures pop up now and again, and have inspired some more modern re-enactors like the ['Frome Spits'] (http://fromespitfiresquadron.blogspot.co.uk/2015/09/where-idea-for-frome-spitfire-squadron.html) and [a group who 'flew' at Goodwood] (http://www.alamy.com/stock-photo-raf-fighter-pilots-combat-training-on-bicycle-at-the-goodwood-revival-38985071.html).