The chances of hitting something vital would be small.
...to non-existent. The V-1 had a rudimentary guidance system based on a Veeder counter, basically it was pointed in the direction of where it needed to go, the counter through revolutions of the propeller at the front wound down until it stopped at which time, calculated as to the time it would take from flying from its departure point to the target area, would cut the fuel lines to the engine and deflect spoilers under the hori-stab to push it into its terminal dive. A two-gyro stabilisation system that actuated the rudder and elevators kept it the right way up.
During the V-1 Blitz, they ended up all over the place across England. I can't remember the statistic but I vaguely remember reading that around 60 percent of those that crashed and were not shot down missed London all-together.
Actually even less than 40 percent made it to London, just looked on the 'net:
"In total,
10,492 V1s were launched against Britain, with a nominal aiming point of Tower Bridge. 4,261 V-1s had been destroyed by fighters, anti-aircraft fire and barrage balloons. Approximately
2,400 V-1s landed within Greater London, inflicting 6,000 fatalities and 18,000 serious injuries."
The V-1 was essentially a cruise missile, a very rudimentary one, but a cruise missile nonetheless.