You are confusing Sea Dart with Sea Wolf.
Sea Wolf is the short range missile capable of destroying incoming missiles, aircraft and shells, while Sea Dart is the long range missile.
Sea Wolf is fired by sextiple rotating launchers or 16 or 32 round verticle launchers, the missile coming in two varients. Only the sextiple launcher version was available in the Falklands conflict, and the system operated outstandingly well. As it did in the 1991 Gulf Conflict.
Sea Dart is fired by rotating twin launchers, and is one of only two(?) such NATO systems capable of automatic reloading in seconds. Whoever said only one missile could be fired at a time, and that they are guided by a 50's era radar, is wrong. The missile and radar entred service in the late 70's with the Type 42's, while the radar has an exceptionally long tracking range, although of conventional design. Due to Sea Dart, in the Falklands the Argentinians (also operating Sea Dart and knowing its abilities), were forced to fly exceptionaly low, to avoid its engagement envelope. The missile didnt rack up many kills in the conflict (which included an unfortunate friendly fire incident on a low flying army scout helicopter). In the Gulf War of 1991 the system successfully engaged two Chinese Silkworm missiles.
Both missile systems are getting a bit old now days though, and soon will be replaced in British service by Aster 15/30.
The verticle launch system for Sea Wolf, is the same as that for verticle launch MICA however, so upgrade is easy.