[Nokose]

Thank you Andrew. I checked again and found that Thorn Island on the Thames River is also called Thorney Island which I believe is near the Royal Palace. Still that doesn't provide help with any better odds in his claim as for the RAF only the following appear.
1 Sqn Hurricane 14:45 damaged in air battle with He 111
92 Sqn Spitfire 14:50 west of Ashford
249 Sqn Hurricane 14:35 West Malling in air battle with He 111
302 Sqn Hurricane 14:45 North Weald doesn't give if fighter or bomber in shoot down
303 Sqn Hurricane ? hrs over Dartford with Bf 109
310 Sqn Hurricane 14:45 over the Thames
310 Sqn Hurricane 14:45 over the Thames
504 Sqn Hurricane 14:45 near Dartford

So here is the German claims outside of the above listed II/JG 2 claims.
Oblt Jerbert Ihlefeld 2(J)/LG 2 Spitfire 15:30 London
(I(J)/LG 2 made three more claims for Spitfires during the day with no names, times & locations)
(Also Stab and I/JG 3 made three Hurricane and two Spitire claims London with no times)
Oblt. Heinrich Sannrmann Stab II/JG 3 Sptfire 15:40 London
Maj. Adolf Galland Stab/JG 26 Hurricane 15:30 Themsemündung
Oblt. Walter Horten Stab/JG 26 Hurricane 15:30 "
Oblt Fritz Losigkeit 2/JG 26 Spitfire 15:40 southeast London
Obfw Walter Meyer 5/JG 26 Spitfire 15:35 London
(6/JG 27 had one unconfirmed Spitfire SE of London with no time, Stab/JG 51 had a Spitfire with no time and location and I/JG 51 had three Sitfires with no times and location)
Lt. Fritz Stendel 8/JG 51 Hurricane 15:28 no location
Spitfire 15:36 "
Fw Gustav Küll 8/JG 51 Hurricane 15:35 no location
Uffz Karl Willius 8/JG 51 Spitfire 15:36 no location
(III/JG 51 had two Spitfires with no times and location. Also a Hurricane with the location of Tonbridge)
Oblt Franz Hahn 2/JG 77 Spitfire 15:35 no location
Oblt Hans-Karl Keitel 1/JG 77 Spitfire 15:40 "
Oblt Karl-Heinz Leesmann 2/JG 52 Hurricane 15:25 Themsemündung
Hurricane 15:40 "
Oblt Helmut Bennemann 2/JG 52 Hurricane 15:30 southern London
Hurricane 15:30 Themsemündung
Hurricane 15:40 "
Oblt. Günther Büsgen 1/JG 52 Hurricane 15:32 no location
Oskar Strack 1/JG 52 Hurricane 15:35 no location
Oblt Robert Göbel 2/JG 52 Hurricane 15:35 Themsemündung
Uffz Heinrich Kooerschläger 1/JG 53 Spitfire 15:50 NW London
Fw Walter Scholz 3/JG 53 Spitfire 15:50 10 km south of London
Oblt Ignaz Prestele 2/JG 53 Spitfire 15:55 10 km " "
Lt Wolfgang Tonne 3/JG 53 Spitfire 15:55 "
Uffz Heinrich Rühl 1/JG 53 Spitfire 15:58 south London
Oblt Jakob Stoll 9/JG 63 Spitfire 15:33 no location
Lt Erich Schmidt 9/JG 53 Spitfire 15:36 " "
Oblt Franz Götz 9/JG 53 Hurricane 15:40 " "
Gefr Hans Swietlik 13(Z)/LG 1 Spitfire 15:10 " "
Obfw Heinz Langenberg 5/ZG 76 Spitfire 15:25
Lt. Werner Pistor Stab II/ZG 76 Spitfire 15:45 10 km SE London

Okay with the all these claims and only six Hurricanes and one Spitfire lost (also the damaged Hurricane) the Spitfire of Hahn's is very unlikely. So the 15 Sep 1940 was not a good day.