I've only been afloat in Littlehampton/Arun a couple of times, but I remember very strong tides up the river, so depending on what type of SIB/engine combination you're going for, make sure you do get the tides right! My only "SIB" is a tiny Avon Redstart with 2hp as a tender to the sailing yacht, and I know that's not going to make headway up the River Arun if the tide is racing out!
If Littlehampton is going to be your main boating area, would be worth seeing what local RYA training centres there are based on the river. Assuming you haven't already done it then maybe doing a Level 2 course with them would be a good idea, which would cover all of the "general knowledge" type things, safe boat handling, and a lot of local knowledge for that specific area.
"Rocking up" and using yacht/sailing club facilities - depends what facilities you're talking about. Most of the ones I've used or been a member of wouldn't really be expecting non-members to turn up and start using their slipways for launching, leaving trailers/cars lying around, etc., and may not be equipped to deal with that. If they have the pontoon/mooring space, many clubs will welcome visiting vessels and/or have reciprocal arrangements with other local sailing clubs, but may want to charge something for usage, given their members pay for the equivalent usage. As above, assuming you're thinking of a few places in particular, e.g. Arun Yacht Club, just give them a ring and see what their visitor/guest policy is.