Plenty of dry stack options in Portsmouth Harbour. From East - West....
KB boat park - Old Portsmouth. Nice spot, couple of nice pubs within a moment's walk for a post outing drink. A few hundred meters from the Solent.
The Dry Stack at Trafalgar Wharf - massive facility, very close to the M27. But a bit of a trek down the harbour to get out to the Solent.
Gosport Marina dry stack - the traffic can be a bit of a pain, but a nice yard with a nice waterfront bistro on site.
I gather there is a new dry stack coming soon to Royal Clarence Yard, Gosport. (Victoria Quay dry stack) - another to keep an eye on.