Hi it gets packed by walkers, fisherman and holiday makers winter, spring, summer, and autumn.
Taddiford Gap after Hordle (small car park set back and long walk through fields) use to be used by a few, but since the storms the cliffs have been eroded and I believe not many people go there now.

I've never swum east of Milford as it's part of Hurst Spit and there may well be strong currents there.
However, I'm a regular skinny dipper at Hordle Cliff (half a mile west of Milford) and swim there all year round - I usually go in just past the last of the beach huts. Despite being overlooked by a clifftop path, the slope of the shingle means you're often obscured from view at the water's edge.

Taddiford Gap is another half mile or so west of Hordle, a narrow shingle beach backed by muddy cliffs. It's an established unofficial naturist beach with a number of regulars. I walked up there yesterday to check out the winter damage as there are often mud slides and cliff falls. More worrying is the gradual disappearance of the beach along this stretch and a few more years of winter storms could see stretches where there's none at all.