The 516 in South Shields (not sure if its still going) used to have an odd timetable, departing slightly later each hour to account for the amount of time a round trip takes and to keep it a 1 bus service. I can't think of any more off the top of my head that is similar.

The old 938 (Sunderland- Tunstall Bank Estate) used to have a break of an hour in the middle for the drivers break (1 bus and 1 driver all day).