But now you've mentioned it, I'm not sure I can think of any circumstances when the safest thing to do is to exceed the speed limit. There will be occasions when it happens accidentally or because you simply want to, in which case the ISA will warn you. But safest??
I will admit that occasionally I will misjudge an overtake and realise the an oncoming vehicle is approaching faster than I initially realised. He may even have speeded up.
Often the safest option is to increase speed to reach your intended safe landing space that much sooner even though it seems illogical to increase your closing speed. On these occasions I concentrate on getting to safety, not whether i will be exceeding the speed limit, or setting off beepers. If I am spotted and reported for speeding, or dangerous driving then its my own fault. It CAN be safer than aborting an overtake by slowing down and hoping someone else will make room for you . But its a judgment call, and you are in the predicament because of previous poor judgment
. Sometimes, regardless of breaking the speed limit it can be safer to drive with confident speed rather than being over cautious and dithering . When merging with faster traffic for instance. Thats why you can fail the driving test for failing to make progress.
Once, soon after i bought the mk4 I accidentally left a 40 mph speed limiter active. When It changed to 60 mph limit I went for a perfectly safe overtake, but hit the limiter ,which suppressed the cars responsiveness. Fortunately I had time to overide it by pressing hard on the throttle. I can tolerate being bleeped at as long as the car remains responsive.