Four years on, it looks as though additional capacity is now required. Prior to the Christmas slowdown in the last week or so, the car park has been pretty much full by 08.30.
Welcome to the forum, DrakeHouse. We have a number of members (and lurkers too!) from Nailsea on the forum, and I'm sure they'll be able to give you an update on the specific parking issues there - as well as other improvements which have been hindered by the station's location up on the embankment.
On car parking in general,
GWR▸ have been relatively innovative in getting it increased, but as theirs is only a franchise for a limited period and car park investment is for the longer term, arrangements need to be in place to have the car parking investment back to them should they no longer be the organisation leasing the station and running the trains. And that's a particularly hot issue at the moment, with no announcement yet as to who'll be running the trains from 1st April next year, and GWR's parent company looking for short term returns across many of its divisions even at the expense of longer term development.