Norwich to Sheringham trains. They go south east and then east, before branching off the Yarmouth/Lowestoft line heading north, albeit north east initially.
Also, the few Nottingham to Norwich trains that run via Loughborough and the Oakham line. Back in 1993 I remember most of them going that way.
The new(ish) Blackburn-Manchester Victoria services via Todmorden have got to be a big contender. It goes completely the wrong direction until Todmorden.
I suppose you could add Leeds trains leaving Lancaster. They head north up the WCML before branching off at Carnforth.
Finally Bristol TM-Avonmouth/Severn Beach services leave TM to the east first.