I was on Weston Mouth Beach, which is not far from there, in July and a few nudists including myself. That maybe a better beach for nudists. I had also seen that Haven Cliffs was listed on a website as nudist but not been.

Haven Cliffs Beach is popular with local naturists but never very busy, perhaps a dozen at the very most along the whole stretch which runs some way. Access is much easier than Weston Mouth despite a relatively long walk on quite large stones.

How far along the beach does the naturist section start? I don't suppose there is any notification as its unofficial. 

There's no notification. Just walk for about ten minutes from where the river joins the sea at the eastern end end of the harbour.