Nothing around lymington, you might want to try hurst castle near keyhaven. Havnt tried it myself but it is worth a bash, dont go out near the spit, there is a raging current. Try the bay near the lighthouse.
chris
Hmmmm, looks interesting. Also looks like you need a boat to get out there or a 4x4 to go along the sands, if you are allowed. If not looks like parking up at Saltgrass lane & New lane & walking across the bridge, then about 1500m walk, or could jump in just after you walk across the bridge.........