I haven't done this on my Rover, but had something similar on my Volvo.
The top and bottom probably have little locking tabs on them - they will not just fall apart. Even with the screws all out the tabs held the two together very solidly.
I pressed along the seam between the two halves of the cowling top and bottom to find where the tabs were and gently prised apart with the blade of a knife.
It may be worth checking that there really are only 3 screws (sounds about right) holding the two halves together, of course.
Steve, March 2008