The first thing you have to do here is define what a defeated RAF looks like in 1940. The Battle of Britain was about the RAF being able to maintain an effective defence force, Fighter Command is key, therefore a defeated RAF is a defeated Fighter Command. The only aircraft that matter to the British are the Hurricane and Spitfire in this fight. So the real question is how low can Fighter Command go in the operational number of these vital aircraft and still maintain an adequate defence?
The low point historically was after the first week of September, roughly speaking 600 operational, 200 non-operational with the squadrons, 100 in reserve, 80 with OTUs and 40 or so with recently formed squadrons that were nowhere near ready to fight. That's just over 1000 aircraft.
The vital defence area was the south east of England and historically was defended by 30 of the 48 Hurricane/Spitfire squadrons in 11 Group, Duxford in 12 Group and Warmwell in 10 Group. If defence of all other areas of the country is sacrificed and all on type training suspended that would mean an absolute bare minimum of roughly 480 Hurricanes/Spitfires available to Fighter Command. So the Luftwaffe needs to inflict 400-500 more casualties on the RAF by mid September 1940 for their defeat to be inevitable. Hope my logic makes sense.
Works for me.
I came to the conclusion a long time ago (I've been working on this conundrum for eight years now) that technical changes were not the answer for the Luftwaffe and that the only way to improve things would have to be found elsewhere.
A few proposals in this thread so far:-
No Bf110 - To me this is not an option, it has an effect on earlier campaigns such as Poland, Denmark, Norway and the early stages of the Western campaign that mean these would be entirely different and could well result in heavier losses to the Luftwaffe. There could have been the development of an alternative heavy fighter but it would have to have all the capabilities of the Bf110 AND be a superior dog fighter to make a difference. Is that possible??
Bf 110 does not offer anything vs. Poland and Denmark that OTL Bf 109E3 will not supply - both of these countries not only have had inferior aircraft, but their airforces were far smaller than LW.
Further, it is not a choice between Bf 110s or nothing at all - choice I favor is that each Bf 110 is replaced with twice the number of Bf 109s, that would atrite Polish and Danish defences even earlier.
Norway differs only in that that it involves long ranges, where the OTL Bf 109E-3 cannot contribute. However, this is where a drop-tank outfitted Bf 109 can be useful (= technical improvement matters). Norwegian AF sported a handful of Gladiators, those will not make a dent big enough on LW bombers that were either as fast or faster.
Much more Bf 109s with drop tanks also means earlier defeat for the air forces 'of the West' after 10th May 1940.
The Bf110 as ground attack only - As I've already pointed out the 110 was twice as likely to come to harm in the ground attack role than the escort role. Losses would be unsustainable. Added to that I'm not sure how effective this would be... the fighter bomber phase of the actual battle showed that as a tactic it achieved nothing of significance, meaning it would have to be supplemental to regular bombing missions. In this case where do the extra escort fighters come from to replace the Bf110s? This is a pure Bungayism, poorly thought out and researched, but with enough surface credibility to be believable. His suggestion of raids on radar installations might have some merit but it would only take one seaborne raid to recognise that the vulnerable point is the little hut where all the vital communications and power equipment is rather than the big latticework of masts. From that point on regular air raids could target these buildings disrupting the network with far greater effect than risky commando style raids.
With no Bf 110s, the ground-attack Bf 110s are obviously never created nor used.
Ju88 as a fast bomber - This is one of those that might or might not have an effect. On the plus side there will be more Ju88s available (if you're not having to redesign the aircraft for an internal bomb load) to replace the Do17. A raid would be able to penetrate a little further inland before interception and carry a heavier load. On the down side bomb accuracy may be a little less, the aircraft will not be able to take quite so much damage or evade attack by out diving opposing fighters and the extra inland penetration only applies to the first wave of any raid meaning they will still need fighter escort.
LW bombers will need escort, indeed, even if we have a 500+ km/h Ju-88 for the BoB.
Long range fighters - Why? Okay, so a bit of extra loiter time is always a good thing but the Bf109 had the range to get to all potential targets in the south east of England. The whole notion that the 109 struggled to get to London is a bit of a red herring, this only happened once the Luftwaffe started massed raids on London where the 109 was wasting fuel in the skies above France waiting for the large formations to form up. On other occasions escorted bombers reached Debden, escorted an aborted raid to Duxford and hit other targets north of London regularly.
Long range fighters are needed to escort bombers, where the mission planer has more elbow room for changing weather, mistakes in navigation, enemy response etc. Having more fuel allows for catching enemy during climb and formation, rather to wait for him to pounce.
Birmingham, for exampe, is 100 miles forther north-west from London and 90 miles w-n-w from Duxford.
Better fighter armament - This may have merit but it's something I've personally never considered before. I guess it's worth exploring further but a cautionary note; fighter command suffered about 1600 aircraft casualties from the start of the western campaign, roughly 1000 of those directly attributed to the Bf109, any weapon improvements therefore need to produce a 150% increase in casualties assuming such improvements are ready from the start of the western campaign.
No single improvement of the LW fighter force will produce such a big increase of FC losses. However, a combination of longer-ranged Bf 109s, more of them already in 1939, more ammo for cannons, better total firepower, less aircraft and aircrew losses in May-June 1940 can snowball hard against RAF FC come July 1940.
RAF in France will be feeling the heat already by 10th May 1940, and LW fighters will be in position to challenge RAF above Dunkirk much better than in OTL.