It's not the most boating-friendly but of seaside, but if you're OK to launch across a steeply shelving shingle beach you could try Madeira Drive just to the East of the pier, or by the King Alfred Centre in Hove. In both places you can park next to the beach. Car parking is less extortionate if you go for the Hove option.
Alternatively you could launch at Shoreham. There's parking by the life boat station and you can launch off the beach. There's an easier option by the old Adur Outdoor Activity Centre a bit further up the river which has free parking. Both are better above half tide, but manageable with a SIB at all tides if you're determined.
Another option would be to drive about 45 minutes to Pulborough where there's a slipway onto the River Arun if you fancy something more scenic.
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