Not a WW2 historian but the Mustang v V1 Bomb story caused me to have a deeper look on the internet.
I think you will find a lot of Mustangs intercepted the V1
"One hero of the V1 campaign was a Polish Warrant Officer pilot named Tadeusz Szymanski, who was on constant Diver duty during July 44 in his Mustang belonging to 316 Squadron at West Malling. One incident involved a frantic chase across Kent on the evening of July 12th, when he was out of ammunition and flew alongside to take a closer look.
"The thing was jerking along and the elevator was flapping with each vibration of the crude jet motor" he said. "I noticed that on the front of the bomb was a silly little propeller. It looked ridiculous. I decided to tip it off balance." Wing under wing, he tried to flip it over but it proved stubborn and just carried on. Szymanski was more stubborn and he made 11 more attempts but they both continued to fly on side by side. "I tried a different manoeuvre, this time hitting very hard with my wingtip as I went into a loop. When I recovered, I found to my dismay that it was still flying, but I had turned it upside-down!" Suddenly, the bomb went into a steep spin and plunged to the ground. Szymanski, more than pleased, sped off home to West Malling.
Szymanski went on to intercept many more V1's and his heroics earned him the admiration of the Polish leader General Sikorski. Later in life Tadek, as he was known, settled in Norwich with his family and became a printer. He died in February 1992.
What a courageous man!"
And from Wiki
"In daylight, V-1 chases were chaotic and often unsuccessful until a special defence zone was declared between London and the coast, in which only the fastest fighters were permitted. The first interception of a V-1 was by F/L J. G. Musgrave with a No. 605 Squadron RAF Mosquito night fighter on the night of 14/15 June 1944. Between June and 5 September 1944, a handful of 150 Wing Tempests shot down 638 flying bombs,[28] with No. 3 Squadron RAF alone claiming 305. One Tempest pilot, Squadron Leader Joseph Berry (501 Squadron), shot down 59 V-1s, the Belgian ace Squadron Leader Remy Van Lierde (164 Squadron) destroyed 44 (with a further nine shared) and W/C Roland Beamont (see above) destroyed 31.
The next most successful interceptors were the Mosquito (623 victories),[29] Spitfire XIV (303),[30] and Mustang (232). All other types combined added 158. Even though it was not fully operational, the jet-powered Gloster Meteor was rushed into service with No. 616 Squadron RAF to fight the V-1s. It had ample speed but its cannon were prone to jamming, and it shot down only 13 V-1s.[31]
In late 1944 a radar-equipped Vickers Wellington bomber was modified for use by the RAF's Fighter Interception Unit as an Airborne Early Warning and Control aircraft.[32] Flying at an altitude of 4,000 feet (1,200 m) over the North Sea, it directed Mosquito fighters charged with intercepting He 111s from Dutch airbases that sought to launch V-1s from the air."