The Cornish Main Line between London Paddington and Penzance is probably the only major route where clockface timetables do not apply (although Far South West departures leave Paddington at XX:06 the pattern West of Reading is somewhat more erratic).
Along the Dawlish Sea Wall the local service has irregular gaps of between 50 and 70 minutes between trains west of Dawlish Warren (e.g. Dawlish departures are at 11:16, 12:27, 13:24, 14:27 etc.) because of the need to allow faster London to Penzance services to overtake at Dawlish Warren.
West of Plymouth there is no clear pattern either. FGW departures are at:
07:02, 08:14, 09:21, 10:42, 11:20, 12:39, 13:11, 13:53, 15:12, 15:57, 16:29, 17:06 to Liskeard, 17:23, 17:55, 18:17 to Liskeard and 18:42 with origins including Plymouth, Exeter Central, Bristol Parkway and London Paddington via Berks and Hants or Bristol.
Also the Settle & Carlisle departures from Carlisle are not clockface either, but are roughly every 2 - 3 hours.