Lots of money and the will to do it...probably does not get done before the end of the war, perhaps a joint US-British project. It probably delays the A-Bomb a few years.
If Britain had developed rocketry/jets more before WWII, how farfetched would it be for the British to retort to V1/V2s instead of night bombing, specially by 1941/42? The UK couldn't produce as many aircraft as the USA and they didn't have as many teenagers to send to battle either. Rockets use no manpower and a V1 type of rocket still ties up AAA and fighters to intercept them. The problem, I think, it's the range.
I always saw the V1 and V2 as weapons of 'Desperation'
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The allies do have an equivalent to the V-2. It is called the Eighth Air Force.
Plus maintenance/repair costs and crew. It's not that anyone would shy of casualties in WWII, but that manpower could be used elsewhere instead. But first they'd need to tackle range - a British V1 would need to have the range to reach GermanyRange and cost.
The V-1 was relatively cheap (about 3% the cost of a Lancaster), but had no legs at all and was less accurate than even Bomber Command's night area bombing. Even then, the ROI was very poor. It took ~10 V-1 to carry the same bomb load as a single Lancaster and every one of them was a 100% loss upon launch. It doesn't take long before the manned system becomes less expensive. This doesn't count personnel losses, but that sort of math is not uncommon in wartime.
Plus maintenance/repair costs and crew. It's not that anyone would shy of casualties in WWII, but that manpower could be used elsewhere instead. But first they'd need to tackle range - a British V1 would need to have the range to reach Germany
On the surface-to-air missile (SAM) front the British apparently used cordite powered rockets from the already existing Unrotated Projectile and RP-3 programmes when developing their Brakemine missile during the war, post-war they moved over to High Test Peroxide (HTP) and kerosene powered rocket engines which became something of a speciality of theirs. Considering that they were able to put a satellite, Prospero X-3, into orbit with a HTP and kerosene powered rocket is there any particular technical barrier to using it as fuel for an early SAM? In a timeline where say the British decide to look into rockets earlier and discover that HTP can be ignited by simply pumping the HTP through a silver plated nickel gauze as a catalyst it would seem to be a rather promising avenue to investigate.
While in the USA Goddard was a prophet in the wilderness, his ideas took root in Germany. If you get as much rocket interest in the USA and even a small amount of government seed money you could have the USA capable of producing a V2 type weapon by sometime during WW2. As has been pointed out, the issue is not was it reasonably possible but why would the USA bother, even if they could spare the resources (and they probably could).
Agree on most of what has been said about the allies not really needing any V1 or V2s - Bomber Command and 8th Airforce did it better (which really tells how lousy/costly V1 and V2 were)!
But if we nevertheless shall try to find a PoD to have allied V1 and V2s it could be:
When Barbarossa kicks in the door the whole house actually come crashing down (don't mind how - just happened OK).
Anyway the Germans have plenty of resources to make a traditional bombing campaign over Germany be way too costly and the allies have far too many warships for the Germans to have a realistic chance of invading the British Isles any time soon.
In such a situation I guess the allies (too) would be motivated to develop somekind of ballistic missile to penetrate the countless Jägerstaffel of Luftwaffe.