The May 1967 event was caused by an intense solar storm which severely degraded BMEWS, which was considered likely to be the precursor to a sudden attack.
Nothing like as serious, but I was on the Stn Ops Desk at Wattisham in 1983 when all of a sudden a similar warning went off. Next thing we knew was the 2 QRA F-4s checking in preparing to scramble. I told them to wait 60 sec whilst I queried with SOC. A flash call to them and they confirmed no alert, real or exercise, was in force. I demanded an authentication, which was correct, then stood Q down to normal readiness with another authentication.
Once they dismounted, their Q-boss (can't remember the correct term) rang and demanded to know the reason for the alert. I assured him that he wasn't the only one asking that question.
It turned out that some numpty was checking the cables somewhere off-station and the test had set off the system - it seemed he hadn't even told his supervisor that he was doing a check....