She would not name any of the alleged victims "due to the pending nature of our investigation", but it was thought there had been a recent rise in alleged hacking of stars, initially reported earlier this year.

Scarlett Johansson: nude photos of the star have appeared on the internet. Credit:Getty Images

The pictures of Johansson, star of Lost In Translation, the Girl with a Pearl Earring and the forthcoming The Avengers, showed her in a state of undress in a home setting.

In one she was holding a towel around herself with face to the camera, her unclothed rear view clearly visible in a mirror, while in the other she was topless. In the first picture she was photographing herself with a smartphone camera, and appeared to be doing so in the second, on a bed.

A publicist for Johansson did not respond to a request for comment.