I am problem going to chewed out for this but..........................
Hurricane I, which is what we are talking about in 1939-40 has a few technical things wrong with it as far as light bomber or fighter bomber goes. Some could have fixed had different decisions have been made at the time/s in question. A few of them apply to the Battle also which is part of the reason for the Battles poor reputation.
There are some other reasons like poor training and/or doctrine and some of them are just ignorance. Like very few people knew how effective light AA was going to be. Germans guessed better than others but they didn't
know despite Spanish war experience.
British and French rather ignored WW I experience or remembered it as too costly and there for not to be repeated. It was too costly to use as a day in/day out substitute for artillery. It was not too costly to use for several days at a time to either push and attack through or to prevent a breakthrough while reinforcements were rushed into threatened areas.
British wanted that short field performance which meant light wing loading which equaled large wings, which means more drag and a bit more structural weight. Battle and Blenheim could fly closer to 60mph than 70 or 70 plus. This made them easy to fly and land but hurt top speed. The flaps didn't offer lot of extra lift. They helped land the planes by using drag and slowing the planes down rather than having them float over the fields if they came in even a little hot. For take off the British hurt the Merlin by giving it that high altitude supercharger. High is relative in 1939-40, Merlin III peaks around 4000ft higher than HS 12Ys or early DB601s but with 87 octane fuel they had to close the throttle to keep from over-boosting the engine and the Merlin III was only good for 880hp for take-off. Which kind of sucks for trying to get even a 500lb bomb load out of small airfield with even the 260sq ft of the Hurricane.
Things the British could have done in 1939/early 1940 that do not require using more modern aerodynamics than the 1935-36 aerodynamics used by the planes (changing structure/shape is going to delay production/service use) is using constant speed props instead of two pitch. Better climb/thrust at low altitudes and less than max speed.
Battle was designed as strategic bomber with a 400 mile radius or over double what the Hurricane could do. It was also designed to fly at 15,000-20,000ft, not sea level or at 1000ft across Belgium. Had the British installed either a medium supercharger gear or a low altitude supercharger gear they could have had somewhere around 1000-1100hp for take-off or combat flying at low altitudes even on 87 octane fuel. Use of 100 octane just adds a couple of hundred HP more. Use the fuel that suits you. It can go either way in the spring/summer of 1940. Please note that were either experimental Merlin's or service engines with both types of gears at the time. Like the Merlin VIII used in the Fulmar. You do have to change production priorities and I am not going to say if that could or could not be done. But the engines either existed or calculations as to power output existed at the time.
No saying that Hooker could have/should have developed the Merlin XX even quicker.
Those are some of the problems I have with the whole Battle vs Hurricane F/B argument. The Battle was never upgraded or given much in the way of protection or extra guns (a few got a single gun firing out through the floor, effect unknown). Hurricane II fighter bombers got the Merlin XX engine with the two speed supercharger, the Rotol propellers, 100 octane fuel and 12lbs of boost, some minimal fuel tank protection and some armor and BP glass. Some really late Hurricane had several hundred pounds of armor around the radiator and cockpit floor against ground fire so comparisons to losses sustained by Battles aren't really valid. That 400hp boost the Merlin XX gave for take-off over the Merlin III in the Hurricane I
was a real game changer as far as getting loads out of crappy airfields but then a 45% increase in power will do that for you
I will note that the Hurricane F/Bs were not doing well in the attacks on France in 1942 and that was the reason that the Whirlwinds were finally given bomb racks. There were only two Hurricane Fighter Bomber squadrons (there were only two fighter bomber squadrons total but that is another story) in operation crossing the channel and such was rate of supply to over seas theaters (or to Russia?) that the existing rate of attrition was going to require at least one of them to disbanded. By mounting bomb racks on the Whirlwinds Fighter command doubled their number of fighter bomber squadrons for cross channel attacks and the reduced work load meant both Hurricane squadrons could remain operational with the reduced need for replacement aircraft. RAF was trying to use small number (not even squadrons size) of fighter bombers as 'bait' for the Luftwaffe while providing several dozen or several scores of non bomb carrying escort.
I tend to like "what ifs" that are about different choices that could have been made using pretty much existing technology of it's time. Jet powered radar equipped night fighters using missiles in 1940 are well into the land of fantasy, not "what if".