Air carrier Captain reported after push-back that the set brakes instruction from the tug driver was not given. The tug was disconnected; aircraft began to move; and the Captain safely stopped the aircraft.

Narrative

Aircraft X was a flight pushing back from [Gate] XX; ZZZ-ZZZ1; full aircraft. We were able to obtain an on time departure. I established communications with tug driver. The connection was working. The tug driver spoke English; but it was hard to understand. However; communication was established; push clearance from RAMP TOWER was received to push and disconnect at spot XX. I queried if Ground was ready for brake release; he said they were; I released brakes and then gave instructions to push to spot XX. The instructions were read back. As tug driver commenced push; I was concerned about how close our left wing was getting to another aircraft. He stopped and then began to pull us forward to spot XX. I had a wing walker in view near the tug; in clear view from the flight deck. I asked if we were clear to start engines (as this was a short taxi and we needed a 5-min warm up). The tug driver never answered. I then got a garbled response; but was not clear what was said. I asked the co pilot if he understood and he did not. We chose not to start engines until we knew it was safe. Then another radio call came through we were able to start engines. We started engine 2 followed by engine 1. We then came to a stop… the co pilot and I recognized that we were not at spot XX. A long silence followed. I called the tug driver a number of time with no answer. I looked down to the wing walker that was in view the majority of the push; but he was nowhere to be seen. Then; I attempted to use the GROUND CALL button to alert crew. No answer. After a moment; we began to move again… the co pilot and I figured we were being pulled up to spot XX to be disconnected. That was not the case. The plane was moving forward under its own power; the tug driver instructed the ground crew to disconnect the tow bar without instructing me to set brakes… all of a sudden a garbled STOP AIRCRAFT was heard from the tug driver. The airplane was disconnected from tug with out the parking brake set and the aircraft rolled forward under its own power with ground personnel in close proximity of nose wheel. This was a DANGEROUS situation. I stopped the aircraft; set parking brake; opened to window to see if everyone was okay. Communication was then reestablished with tug driver. I said I never received instructions to set brakes. SOP was NOT followed. I said the headset had failed and communication was lost. I asked the tug driver to fill out a report that the headset does not work.