As you say, the Luftwaffe had largely switched to night bombing by the winter of 1940, but daylight operations had not ceased entirely. The Ju 87 Stuka had, for the most part, been withdrawn from operations in August due to the heavy casualties they sustained, but a few squadrons started anti-shipping operations again in November 1940 with fighter escort and scored some successes against merchant ships, requiring defensive patrols over shipping. Fighter-bomber ("Jabo") variants of the Bf 109 also continued to make daylight attacks, typically flying at extremely high altitude with fighter escort, into December, so Spitfire and Hurricane squadrons were still regularly scrambling.

Fighter Command also operated night fighters. It was poorly equipped for the start of The Blitz with a few squadrons of radar equipped Bristol Blenheims (generally ineffective, with the earliest Airborne Interception (AI) sets being unreliable and short ranged, and the Blenheim itself barely being faster than the German bombers it was hunting) and Boulton Paul Defiant turret fighters, withdrawn from daylight operations and somewhat successful in the "Cats Eye" role, using moonlight or searchlights to find enemy aircraft. The inability of Fighter Command to effectively combat night bombing was a matter of some consternation, and a primary reason (or excuse, at any rate) for the removal of Hugh Dowding as C-in-C at the end of November. The introduction of the Bristol Beaufighter - faster and more heavily armed than the Blenheim, with improved AI Mk IV radar - coupled with Ground Controlled Interception (GCI) radar finally gave Fighter Command a potent weapon against night bombers, though it took time for production to scale up and for crews to be trained so there were also a variety of more desperate schemes including flying Hurricanes in the "Cats Eye" role, mounting powerful searchlights to radar-equipped Douglas Havocs, and the Long Aerial Mine - a lengthy cable mounted on a Havoc with an explosive charge on the end, designed to be dangled in the path of enemy bomber formations.

From December, as the Stuka and Jabo operations wound down, Fighter Command took to the offensive. Under its new C-in-C Sholto Douglas it adopted a strategy of "Leaning Forward" over France in addition to the defensive operations that remained its main purpose. There were various types of mission including Rhubarbs (small numbers of fighters or fighter-bombers making low-level sweeps), Circuses (a comparatively small number of bombers heavily escorted by fighters with the intention of drawing the Luftwaffe up to fight) and Roadsteads (escorted anti-shipping strikes), intended to instil an offensive spirit and tie down German resources. Continuing through 1941 the strategy seemed to be effective - the RAF claimed 731 German aircraft over June-December 1941 for the loss of 411 pilots - but the problem of overclaiming that bedevilled all air forces was particularly bad in large combats over enemy territory where results could not be observed, the Luftwaffe only lost 103 aircraft to fighters in that time. In many ways it was the reverse of the Battle of Britain, the RAF fighters operating at the edge of their range against an adversary who could pick and choose optimal engagements.