I know that they were able to target London, but what was the limits of their accuracy?
Southampton was targeted by a small number of V-1s; according to Stephen Zaloga's V-1 Flying Bomb 1942–52 65th Corps fired 53 V-1s from ground launchers against ports in the Portsmouth-Southampton area, but were reprimanded for not following orders to concentrate on London. He doesn't state how many, if any, hit the area. There were also air-launched V-1s carried by He-111 bombers; 300 aimed at London, 90 at Southampton and 20 at Gloucester. Of these "... none hit Gloucester and British authorities thought the shots against Southampton had been aimed at Portsmouth". Only half landed within 25 miles of their target.
After the Allies captured Antwerp it was subjected to a bombardment almost as heavy as London (10,332 V-1s were launched against London, 8,696 against Antwerp). Of these only 4,248 actually reached the Antwerp region, and only 211 fell into the port area. Between the unreliability of the V-1 (up to a quarter of the flying bombs crashed prematurely), inaccuracy of its guidance system, and Allied air defences (1,766 of the Antwerp-targeted weapons were shot down) it was not a useful tactical weapon.