While it's not quick, you can do Portsmouth with one change at Southampton or Guildford, or Brighton changing at Redhill.
You can also change at Basingstoke for the Portsmouth Harbour train. My problem was, until the newly restored timetable, was coming back via
BSK▸ when the Reading Flyer was an hourly service, and I would inevitably end up spending 50 minutes at BSK.
Getting to Eastbourne can be more challenging with the ongoing improvements at Gatwick.