Reading the WECA» rail plan a few years back, I got the impression that doubling this junction might be all that was needed to get to 3tph to Avonmouth.
Looking at Real Time trains for today, the 13:00 from Clifton Down (a random train) arrives in Avonmouth at 13:12 and that 12 minutes includes a half minute performance element. It calls at Portway Park and Ride at 13:10. I note it calls also at Sea Mills and Shirehampton. I note that the double track into Avonmouth starts a bit of a way out but the line goes single as it leaves Clifton Down.
This suggests to me that a service every 20 minutes would work, tight, with 2 stops between Clifton Down and Avonmouth, but not with three without other interventions. Those could be such things as
* Electrify the line to get better acceleration of trains
* Have just 2 stops, alternate trains (so 40 minute service, or 60 minute if you want clock face) at Sea Mills and at Shirehampton
* Extend the loop at Clifton Down into the tunnel (but that would mean trains waiting in the dark for the single line)
* Extend the double track at the Avonmouth end - but that would mean it being doubled over a level crossing and probably a second platform at Portway Park and Ride
* An intermediate signal would allow 2 trains one way then two the other, but that would then be "three trains an hour" and not a regular 20 minute service.
* An Ormskirk or Headbolt Lane arrangement
* Something I have not thought of