Ah, where is wiking when you need him the most? We just had a conversation on this a while ago, and while wiking won't be able to join for a while sadly, he did give some great points, which I feel the evidence strongly favors them along with some expanding details of my own. Note, I'm simply paraphrasing what he has told me.
Let's say a V-1 is launched every 15 minutes. That would be 96 V-1s per day. Let's assume a V-1 killed two people on average and the campaign went for 365 days, a full year. For 96 V-1s * 2 people killed on average hit * 365 days would be around 70k deaths. Around 50% more causalities than the Blitz using fewer fuel, fewer strategic materials and no loss of aircrew at all!
For those that say "this would bankrupt Germany", we should compare the costs of the V-1's lanuched per day for a full year:
96 V-1's * 365 days * 5,090 RM(cost of single V-1) = 178,353,600 RM(Just about the cost of a Bismarck battleship, and remember, no strategic materials are used, just plywood and sheet metal)
compared to the Blitz:
Now I'm going to be generous and use the amount of aircraft lost by using the Bf 110 as an example with just it's airframe with no engines at all. I understand there were cheaper designs such as the Bf 109 and and much higher cost designs such as the He 111, but I feel as if the Bf 110 with no engines is the perfect averaging balance.
Bf 110 airframe cost is 155,800 RM * 2,265 aircraft lost = 352,887,000 RM.
So Germany could spend around half the cost of an flying bomb with no losses to German aircrew, going at it for a full year compared to the nine months done by the Blitz.
Having a V-1 ready to strike London around August/September with no blitz, is a perfect what if unlike Hitler taking a Mediterranean route or appealing to the Soviet citizens as "liberators." This scenario works perfectly for Germany economically. For those who say the V-1 is inaccurate, here is a map showcasing the radius of a V-1 with original accuracy being 19 miles of a radius and then improved accuracy with 7 miles of a radius.
Remember improving accuracy was from June 1944 to March 1945, over a period of nine months where Germany was facing constant heavy bombing from the allies along with even poorer intelligence gathering. In 1940, the Germans would have factories virtually unopposed and could bring the necessary material to bring the V-1s into the production.
For those who say it will waste more resources, you need to understand that when comparing for the cost of the aircraft, others have pointed out that the V-1s need to be simply built and armed, while bombers such as the He 111 need not only their air-frame, but engines, electronics, MGs and a trained crew which takes up more costs for fuel as they must learn to fly the plane many times before heading into combat.
As for those who say that the British morale wouldn't break, using the Allied bombings as an example for how German morale sat still, take a look at how our current government which has played music nonstop to terrorist prisoners and how after days, it would seriously derange them mentally. If they would hear the same music on certain days, while not hearing other days, the mind would be able to have a rest from it being able to interfere with it's cognitive abilities. When we sent thousand bomber raids over Germany, many of them were at night to limit interception, and there would few breaks in between bombings, some nights were left alone, but the the daytime would be peaceful mostly.
In this scenario put forward, Londoners would hear explosions along with the buzzing noises and have buildings destroyed constantly day and night, with virtually NO break in between. I doubt anyone could sustain having a continued 24 hour bombing on their capital receiving no sleep, and no time to even construct a part of the city which will be going on for a year or more. Emergency relief would be constantly overwhelmed, along with fires that could not be put out due to fear of a V-1 missile falling. London would have no time in rebuilding their city and industry, along with massive panic as many Londoners would try to flee the city clogging up railways(Even if a quarter of the population were to leave, 2 million would still significantly choke up the lines, reducing logistics to rebuild the city).