Errors in geography
It literally takes several different safe combinations, known to several different officers, to get the dozen or so physical keys that are then inserted and turned in a dozen different locations.
The sub also needs to go through specific evolutions to prepare for the launch of a missile, such as mandatory depth, speed, and trim limitations, not to mention the launch control must sequenced specific buttons and switches in specific ways at specific moments in a countdown process that takes AT LEAST 12 minutes to accomplish once power has been applied to the launch systems.
It would be IMPOSSIBLE to simple press a button on a remote computer and have a ship launched missile OF ANY KIND fire within seconds of a cold start.
Also, the missile travels from it's launch point to impacting the target in 90 seconds. Thus, it traveled at an average speed of 40 miles per minute, or 2,400 miles per hour. Cruise missiles have a maximum speed of 550 miles per hour.
Incorrectly regarded as goofs
It is plausible that the British trackers could think it was a quarrel within the anarchist group, but a single phone-call should tell them differently. Absurd that professional agents should not have this set up.