I suggest you re-read your history of WWII. While, for the Blitz and the V-1 campaigns, Londoners knew what was coming and could shelter, the V-2 made absolutely no noise and gave no warning whatsoever. The Londoners learned of a V-2 arrival when a city block somewhere just blew up. Since they were imprecise, nobody knew who or where the next hit would be. That stress from the V-2 campaign almost broke the Londoners' morale and psychologically affected quite a large number of them. Based on historical research shortly after the war, it was the one campaign (V-2) that caused the most distress to the City's inhabitants in the whole war.
Now take that and the 4000Km range circle and see who could be targeted in the West or the middle east and, unlike the first two aimed at DG who went under the civilians' "Radar", hit a city without warning a few times and the population will be screaming for action, and that would lead to an all out war in the M.E.