Had all these experiences with Southern when I used to commute to East Croydon. In winter, used to routinely have consecutive services running through without stopping. Came to the conclusion that as there is so little turnaround time scheduled at the termini, they resort to running fast (i.e. cancelling the service but try getting them to admit that) when only minutes late as otherwise this trickles through the whole day's schedule.
Tip: if the departure board says 'Delayed' this means the the service running in the opposite direction has not even arrived at its destination yet. Can be useful info if you are prepared to take alternative routes.