There's a few areas to check...
1) Rear brake compensator. Is your spring under tension or loose? Adjusting the compensator (£free) will improve the operation of the handbrake.
2) Cables. The rear cables could be sticking and/or stretched. New ones might help but at £20 a side, I'd leave that until one of the last resorts. Once they're off the caliper, you should be able to easily slide the core in and out of the sheath... put some oil and then grease in there and work it in. If they feel "tight" (bent or kinked outer .. or the inner core liner is damaged.. ) get new ones.
3) Pads worn out. New pads give the handbrake mechanism less work to do. If your pads are down to the last 2-3mm.. get some new ones.
4) Calipers seized or sticking. This is the most likely. You can get overhaul kits if the seals are damaged but a strip-down and clean is the only way to recover them. If the pistons are scored or look beyond help, or if the nipple is broken off and you can't face overhauling them, you can get replacement, reconditioned Budweg calipers from Brakes, brake discs, brake pads, brake calipers - Brakes International Shop
.. all new internals and a shiny freshly re-anodised but previously second-hand body.. on an exchange basis.
They're about £100 each (once you get the rebate) for the alu' calipers.. so probably a last resort.. but they're essentially "brand new" calipers.