Not 70s, but 80s and early 90s, but perhaps of interest. For most of the 80s I remember:
- hourly Portsmouth to Southampton all stations, alternate hours extending to Salisbury (3H DEMU)
- hourly Portsmouth to Eastleigh all stations, alternate hours extending to Reading (3H DEMU)
- hourly to Bristol, alternate hours to Cardiff (33 + Mk-I stock; fast from PSS to Fareham and Fareham to Southampton). From May 1988, 155s took over this service.
Such a pattern was still in existence in early 1990, immediately prior to electrification, though I think by then all services on that line terminated at Eastleigh, no through Readings.
However, in 1981/2 and 1982/3 (source: Timetable World) it appears the all-stations stopper only operated between Portsmouth and Southampton and there was an additional semi-fast hourly (mentioned by the OP) to either Romsey or Salisbury, calling at Swanwick, Netley, Woolston and St Denys - perhaps the last occasion when Netley and Woolston had two trains per hour.
In May 1990 when EMUs (CIGs and VEPs) took over, the standard pattern was a Portsmouth to Poole all stations stopper, and the Eastleigh extended to Waterloo calling at Winchester, Basingstoke and Woking only. I think these two interworked (the timings would suggest that) but I never verified that - can anyone confirm/deny this?
Also in 1990 there was an hourly Victoria-Gatwick-Hove-Southampton Central service, limited stop along the coast.