I want to improve the insulation in our loft as I believe most of the
heat from our radiators is going straight through roof.

Some loose insulation material (rockwool?) currently exists between
the joists to a depth of approx 4 inches, though some areas have no
insulation at all.As I only bought the house this year I have no idea
how old the insulation is.

Am I better off to remove the existing insulation, which would be a
rather messy and dirty job, and start from scratch or should I lay new
insulation on top of the old stuff.

What's the best insulation to use and to what depth. I'd prefer to
over-insulate than under-insulate. It is a lathe and plaster ceiling
and part of the roof has floorboards.
Any advice gratefully received.