I guess I'm viewing the V-1 in this time frame still as a concept of a "terror weapon", which I still think would have made hitler drool with delight in 1940. Only in this time line he would envision them raining down on Paris, once the mobile launchers got within range. Only the quick surrender spoiled it all. So now he directs them against London/southern England with that same intent. Heck, the British could have the V-1 blueprints, but that's not going to do them much good.
The propaganda would be, "we can hit you at will, and good luck finding our launchers, (and secretly hoping the RAF attempts just that), and if you don't come to the table, we will unleash the Luftwaffe". Heck they could probably rig some V-1s to scatter propaganda leaflets.
So the populace, with the BEF defeat in France, and their near destruction at Dunkirk, a recent memory, now find bombs falling on them with no defense. At least during OTL BoB and the Blitz, the British people could see the Germans getting badly bloodied for every bomb that fell. Now, that moral boost doesn't exist.
Again, at this point the weaknesses in the Luftwaffe aircraft and tactics wasn't apparent, so all those planes marshaling across the channel would appear to be a very grave threat. Only in this TL London is already under attack and the British military appears powerless to stop it. Would public, and political, opinion worry that the destruction and loss of life would only get much worse, if the Luftwaffe did show up?
Ric350