But I think you may have drum brakes on the back, or are have you shiny disks through the wheels (when you look) like the front? If shiny you have disks on the back and it may well be a seized handbrake mechanism in the caliper. If drums, he's dreaming ................
No need to do a full inspection, just get the imbalance on the back axle fixed, the NCT have already done the inspection for you/them? Have you got a good small back street independent mechanic that can take a look for you?
Don't mean to be awkward, but better to put the money towards the actual fault, already listed