Check and see if there is any play in the cable. Another possibility is the drums are needing adjusted
Removal of rear wheels is required,
It's an easy process (assuming the adjuster turns), there is a hole in the hub section of the disc thats slightly bigger than the wheel bolt holes and if you rotate the disc until the hole is front of the adjuster wheel (you may need a small torch poked into the hole to verify this) then just use a medium sized screwdriver and adjust up until the disc wont turn by hand then back off the adjuster just enough until the disc turns easily enough again by hand and this is the shoes set up after that if the handbrake lever is still coming to high you can adjust the cable.
In my experience with the 406's the handbrake cable adjustment is usaully rusted up and it's quicker and easier doing the shoes adjustment first.
But as Ian says check that the handbrake cables are ok first, a simple check would be jack up the back wheels and pull on the handbrake and see how well (if at all) the wheels are being held by trying to turn the wheels by hand.