This is the statue of Charles II in Soho Square. It was carved out of fairly soft sandstone in 1681, 330 years ago, which is why it is so badly eroded. Notice his face though: the statue is carved out of a single block of stone, except for his face which is cemented on, like a stone mask. It's a good match, and perhaps replaces a face that was so badly worn or vandalised as to be not much of a face any longer. That face is eroded, but not nearly as much as the original statue.
According to the plaque it was 'Restored to the Square by Lady Gilbert in 1938', Lady Gilbert being the wife of W S Gilbert, of the famous Gilbert and Sullivan musical partnership, and perhaps it was she who decided it was time for the former sovereign to get a facelift.