Yes, absolutely as you say Malcolm
What happens Jason, is that the handbrake cables split and then water gets in and sets up rusting which binds the cables.
Despite looking like a real ***, the job of replacing the handbrake cables is refreshingly easy
If the rears are the problem, pop the pads out and see if they're worn wedge-shaped. If they are, it's a sure sign the calipers have corrosion behind them. Another dead give-away is if the rear disc does not sit centrally between the caliper halves. Corrosion builds up and actually pushes the caliper off-centre and away from the trailing arm.
Beware, removing the 17mm caliper securing bolts on a badly corroded caliper is a bit of a 'mare. If this is your problem, come back for some hints and tips on loosening these bolts without shearing them. If you don't go in with care it is sadly all too easy to shear them and find yourself in a whole world of pain...