All right - if there was something that Bomber Barons didn't like in 1930s, that was deploying 'proper' RAF aircraft into Army co-operation tasks. The tasks being artillery spotting, tossing a bomb or two/machine-gunning the enemy infantry, trucks & guns, carrying a healty or wounded soldier or two between different Army locations etc. Direct air-defense - not until Dunkirk? So let's give the grunts the 'airforce', that will be comprised by much better A/C than it was the Lysander (and earlier than P-40 or Mustang), while not blowing up the budget. Two A/C can be suggested, since some roles require one kind of aircraft vs. what other roles require. The A/C need to became available by early 1939.
I was thinking about this very thing on the way home yesterday
My idea is that instead of the RAF absorbing the RFC and the RNAS at the end of WW1 - it simply becomes a 3rd air arm responsible for the defence of the Homeland - and has responsibility for AAA - lets call it AAA or Ack Ack Command - of cities and home island defence fighter squadrons - let's call it fighter command and the Organisation Royal Air Defence Force or RADF (pronounced
raadaff). The organisation is upon its inception principally concerned with preventing a repeat of the Gotha bomber raids of England (the Zeppelin threat having been defeated already) and as an organisation treats the claim that "the bomber will always get through" with both contempt and as a challenge to its existence.
Later a 3rd and 4th force are generated - Bomber command and the RADF Regiment responsible initially for the defence of RADF airfields against Terrorist, 5th columnist and Parachutist troop threats against Home island airbases and later assets of the Air defence net work - both coming under the command of RADF.
So how does this help us with the op's question in 1939?
Well in this POD the Navy keeps its airforce and more importantly for this thread the Army keeps it airforce and in our analogous 1939 each of the army corps has a Squadron of 12 Lysander's for Co-operation/recce work/forward obs and a large squadron (say 30 a/c*) of CAS/dive bombers based on the Hawker Hurricane (with only 4 guns but better protection and capable of carrying underwing bombs) - and unlike our OTL RAF do not hold the idea of dive bombing..or loss height bombing as they cynically called it in the late 30s with irrational contempt and are instead in 1939 ready adopters and indeed leaders in the field of dropping bombs fairly accurately on tactical targets like enemy artillery units and troop/supply columns behind the main line of enemy resistance and in direct support of their parent formations fighting divisions.
The a/c being used should be similar to those being used by the RAF.....erm I mean....the RADF and the RNAS as much as possible - or it could be that the aircraft manufacturers split along service lines - ie Fairey and Blackburn traditionally build for the Navy etc etc
*I use 30 as Typhoon squadrons on D-Day typically numbered 30 a/c each - I suspect this was in the expectation of heavy losses and previous CAS experiance!