Portchester SC is great place...opposite Port Solent marina, safe car park and tender storage.
Or Southampton waters, Cracknore SC, just between Hythe and Marchwood...
If you want the very cheapest and it must be strictly the south coast, check out Rye. I haven't been there for a few years now, but it has always had a reputation for low prices. Prices vary, but I think you can get down to about £120 per meter per annum for a yacht 8-15m. Of course these are mud-berths with limited tidal access.
Portchester sailing club.
Club membership, deep water mooring, 24 hour slipway, dinghy storage, car parking, sublift into winter storage ashore etc would probably cost about £700 - £800 (I now get pensioner rates, so a bit cheaper).
I think max 32 foot in the yard and there may be a couple of years waiting list for the yard.
Self help club. If that style of sailing suits then check it out... http://portchestersc.org/