Chronic alcoholics can sometimes develop Korsakoff's syndrome, which causes brain damage. It has little effect on the STM, but severely impairs LTM. This suggests STM and LTM are stored in separate areas in the brain.
Shallice and Warrington
Reported the case of KF who suffered brain damage in a motorbike accident, his LTM was intact, but he had difficulties with STM. Again suggesting that STM and LTM are stored in separate areas in the brain.
Brain scans show differences for different types of memories
Baddeley used brain scanning technology and found distinctly different patterns in brain activity when participants were asked to recall items from their STM and LTM. This again suggests that there are separate stores.