[WOPR (robotic voice)]"Do you want to play a game?"[/WOPR]
One hopes that will never happen.
US ICBM launch control centers have a similar setup called REACT (
Rapid
Execution
And
Combat
Targeting), sometimes derisively called "Windows for Warheads". The actual release of nukes does not rely on a computer. (REACT does not use Windoze.)
More information on REACT:
http://www.fas.org/nuke/guide/usa/c3i/react.htm
REACT makes it easier to monitor the status of and re-target ICBMs in minutes
BTW, Britain does own and control the nukes and the missiles aboard their SSBNs. It was back in the 1960s that the US owned and controlled the nukes and Britain owned the land-based Thor IRBM missiles.
More information on the British nukes:
http://www.fas.org/nuke/guide/uk/slbm/index.html
Practically EVERY aspect of nuclear command and control requires a minimum "two-person concept" - no one person can be present in an area where nukes are present, nor arm or launch nukes. The movie
Crimson Tide shows (if you remove the Hollywood dramatics and implausible scenario that could never happen in real life) how a nuclear control order is received, authenticated and executed.