The report I was quoting (from AIR22/500) reads:
0925–0938
1021–1045
Unit: 4.(F)/123
Number of aircraft: 4
During the first sortie at 1924 [sic] an aircraft was plotted by D/F 27 miles SE of Beachy Head. On the second sortie (3 aircraft) combat seems to have taken place with Typhoons and Typhoon Bombers. 2 aircraft reported that they had received hits, one pilot being wounded, but were able to reach base, possibly Évreux or Bernay.
Obviously we don't know exactly what the listeners were hearing or how far they were trying to piece together indistinct fragments. On the other hand, if the Typhoons shot at two 109s, you think they'd have mentioned it in after-action reports.