At the same time they had to push the german fighter groups back from the Channel, which they achieved, at great cost, but they were successful eventually.
Pushed back..? Huh? Most fighter unitstransferred to the Ostfront in early 1941. A couple of Wing remained. Those remained in the exact same spot for years, essentially fighting like guerllas in the air. I do not understand what you are talking.
Ratio of loss was 1-5 favour of Jagdgruppen, despite outnumbered. RAF was not outnumber in 1940.. it outnumbered attacking fighters in contrast and had poorer results. Of course advantage of Germans was they had nothing to defend in France. Bombing of France by English..? It is a favour for German. France is enemy country.. they can sunbath in airfield, sip beer, watch show. British couldnt do, when London was attacked, they had to fly.
The Germans retained a qualitative advantage especially in the expereience of their pilots, but in terms of organizational skills, I dont see anything that compares with Fighter Command, until the reorganization of the Reich Defences and the establishment of the Kammhuber line in 1942-3. Until then, the Luftwaffe, whilst enjoying a significant qualitiative advantage in its personnel, did not have the organizational skills to match.
I do not think this so simple. The UK had centralized fighter defense system with radars, Germany had a de-centralized fighter defense system with radars. At start of war. The latter worked well enough, Bomber Command forced to cease daylight bombing. Centralised system was better for defense against massed raids, but British system was hardly perfection, it could scramble fighters from a Group, even scramble-able, guided Squadrons number was limited.. but otherwise was rigid area defense.. 11 Group and 12 Group not even working together at all. British had not one home defense system but four! Complete human stupidity and rivalry between leaders, otherwise easily possible. Technically it was limited, radar operator can not tell true altitude, nor could tell true numbers of enemy aircraft - vital elements - too poor training, too poor equipment (big wavelenght CH radar, more primitive, early radar). Completely blind over land - radar only sees to sea. Organistation, "Big Wing" controversy is well known. Some UK leaders realized need for centralised fighter, bomber etc. force. Like Germans already did. British organisation and planning, scramble relied on small Squadron, German already on Big Wing (Gruppe). Different words - German already had system which routinly concentrated force into large units. USA, USSR similiar structure. Only UK relied on ad hoc grouping of Squadrons in 1940-41.. No doubt it was backward practice of WW1. Speaking WW1 - Red Baron already realised that, used Big Wing tactics as English call. In reality, idea present from immerial times: concentration of force. Napoleon was one master of it.