Approach Controller advises Beechcraft 35 pilots they began descent for an approach fix without clearance. Pilots believe the clearance was given and forgotten by the Controller. Cite language barrier.

Narrative

The flight; on an IFR flight plan; was a training flight with an experienced pilot in an airplane he was inspecting for purchase. I was serving as the CFI and pilot in command for the flight; though the other pilot was performing all flying and communication duties. I was holding the checklists; charts and continuously monitoring the instruments to track attitude and position to back up the pilot flying. We requested the ILS 1 approach with a circuit of the holding pattern. We were cleared direct KAREL intersection on the ILS Runway 1 approach at RMG. We were instructed to maintain 3000 feet until established and report crossing KAREL inbound. When approximately 1 mile from KAREL; we began a descent out of 4000 feet. ATC asked us to confirm 4000 feet and we said; 'Negative; we are 3700 feet for 3000 feet as previously cleared.' ZTL responded; 'negative; maintain 4000 feet until established and report KAREL inbound.' When ATC corrected themselves; we immediately pitched up to return to 4000 feet. Then; shortly thereafter; were cleared down to 3000 feet and established in the hold and proceeded to execute a normal ILS approach to landing. We canceled IFR in the air once in VMC with the runway in sight on short final. ATC made no comment about the miscommunication and we do not suspect any deviation as a result of the miscommunication nor any traffic conflict. All communications were clearly read back by the pilot flying with aircraft N-Number. A contributing factor may have been the slow; southern accent of the ZTL Controller.