RevStar - The term "visual approach" clearly means different things to different people.
In the UK it is a means by which a flight may be expedited when the pilot reports that he can maintain visual reference to the surface. As ATCO2 said, ATC remains responsible for the separation from other traffic.
Up until a few years ago we were allowed to authorise a pilot to maintain "VMC and own separation" from other traffic, but this was withdrawn by the regulator on the grounds of being an inappropriate delegation of ATC responsibility.
The only method we have of allowing pilots to provide their own visual separation is by using one of the permissible"reduced separations in the vicinity of aerodromes".
This is used to good effect at Heathrow in suitable weather conditions when both parallel runways are being utilised during arrival peaks.
I cannot honestly see how transferring responsibility for separation to the flight deck could sustain landing rates at airports where High Intensity Runway Operations are performed.