On 20th September 1939 three Fairey Battle bombers of 88 Squadron based at Mourmelon-Le-Grand in France as part of the RAF Advanced Air Striking Force (A.A.S.F.) took off at 10am for a recce flight over Aachen. The aircraft were fired on by French anti-Aircraft guns before they crossed the border. Over Aachen they were engaged by three Messerschmitt Bf109 fighters. Battle K9245 flown by Flight Sgt D.A. Page with crewmen Sgt A.W. Eggington and AC1 W.A.W. Radford was shot down, quickly followed by Battle K9242 flown by Flying Officer R.C. Graveley with crewmen Sgt W.S. Everett and AC1 D.J. John. Flying Officer Graveley was awarded the George Cross Medal for his attempts to rescue his crew from the burning aircraft. In the remaining aircraft, K9243 flown by Flying Officer L.H. Baker and crewed by Sgt L.H. Letchford and AC1 C.A. Edwards, fire was returned by Sgt L.H. Letchford in the gunner's position. He claimed a Bf109 shot down. This does not seem to have been officially "confirmed" at first, which is why the shooting down of the Dornier by Skuas on the 26th is often listed as the first British aerial victory of WWII - It should more accurately be called the first British aerial victory to be confirmed. Evidence to support the claim for Sgt Letchford came later, from French sources, which in turn led to it being confirmed.
I believe the Junkers JU88 shot down by the aircraft of 603 City of Edinburgh Squadron over the Firth of Forth near Edinburgh may have been the first shot down over British soil?