You only have knowledge available at the time to work from .
Starting when, 1935?
Am I allowed to tap only expert opinion from HMG boffins or Service people? Or can I reach into other speculative sources? That is, if (frex) Arthur Clarke wrote about satellites in 1940 (he didn't, AFAIK), could I put somebody to work on it?
That said, at a first pass, I'd be asking the boffins & Service experts about intercepting bombers. How are they going to be detected? How are fighters going to be intercepting them? Are they going to be controlled, & how? (My goal here is radar, & GCI with PPI; that outcome would be unknown at the time, but the knowledge to
get there wasn't.) How effective are the fighter guns against bombers, and are there better weapons? (Again, the goal is the HS.404; getting there is foreseeable, if that goal itself isn't.) I'd also be asking about measures to defeat U-boats, & if there were any already known that might be revived. (There were, including dipping sonar.) In that area, I'd also be wondering about better a/c for ASW patrol, & possible basing options. (The goal, basing in Newfoundland; is it reasonable to imagine RAF basing a number of *Stirling squadrons there in 1939?)
Following on these, of course, is the electronics industry to support production of radar, which would need financing. Aid to the same in the Dominions might also be a good idea. (Is that asking too much?) This has the added benefit, I suspect, of making radio equipment in general better.
In the aeroengine area, I have a sense the Merlin couldn't have happened appreciably earlier, but the Hercules might have, & effort wasted on other projects (Vulture?) might be avoided. Research into aviation fuels would be a good idea; adding tetraethyl lead would be a start, but what about adding methanol as an octane booster, instead? What about even more exotic fuel mixtures, akin to those used by F1? (Too extreme for the fuel chemistry at the time?) And what about methanol or nitrous ijection?
I'd suggest building new a/c & engine factories in marginal districts as a jobs program. (The ultimate goal, producing the latest fighters in wartime; is Germany being aggro enough, yet? Is Winston strident enough?) I'd be inclined to suggest "bribing" the Dominions to do the same, as well as to set up pilot training plans. (Does this require too much foresight?)
Am I limited to home defense? I'd also be inclined to looking at basing in Malaysia & base defense there, especially given the idea a/c were to rapidly augment the defenses. This might also want a look at better a/c-launched torpedoes or ASMs, like Felix. It also wants better TBs.
Am I banned from looking at FAA? I'd want to look at escort carriers, & the prospect of converting bulk grain or oil carriers to escorts, able to operate TSRs. (Am I pushing the limits?)
Going a bit further afield, I'd want to know if the jet engines & guided weapons in pulp novels are in any way credible. (The goal, develop the Whittle engines, *Felix, *V-1, & possibly RPVs.)
In addition, is it credible to examine the RAF's theory of single-engine light bombers, & so avoid the Battle contract entirely?
Have I missed anything?
Edit:
next fighter generation (the Hurricane) to be developed as a sea fighter
Yep, I overlooked this...
I'd send a technical mission to the U.S. to look at naval a/c design, to see what lessons need to be learned, & what U.S. companies can teach. (Unfortunately, this is the period between the F3F & F3A, & before the F4F & F4U, so most of it will be obsolete before the Hurricane & Spitfire reach service...) Would a mission to Japan, & lessons from the B5N, even be possible, or would IJN simply refuse access?