B747-400
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Communication Breakdown; Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Wake Vortex Encounter
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Human Factors; Environment - Non Weather Related
Enroute to Hong Kong while transiting Delhi Airspace we requested a climb from FL310 to FL390. I heard Delhi respond with FL390 not available; climb to FL350. First Officer (F/O) read back 'climb to level 350.' F/O was at the controls and set MCP altitude to FL350; [the relief] F/O verified the altitude on the PFD and F/O initiated a climb leaving FL310 for FL350. We had just swapped crewmembers seats; [relief] F/O replacing Captain in the L/H pilot seat. Captain then went into the cabin for approximately 2 minutes and then returned to the cockpit R/H observer's seat and saw a converging aircraft. Captain initiated evasive response instructions to descend and turn left to F/O. The airplane was not responding as quickly as I wanted; so from the R/H observer's seat; I reached over and disconnected the autopilot; grabbed the yoke and throttles and made an aggressive descending left turn to clear the conflicting aircraft. We encountered the other aircraft's wake turbulence. During the conflict; we had conflicting instructions from Delhi ATC; who ordered us to descend to an altitude (FL320) with another conflicting aircraft; then ordered us to climb back to FL350. I leveled off at I believe it was (FL325) because I knew there were no other aircraft at that altitude; until we could find satisfactory resolution to the events that just happened; as it was all a lot to comprehend and decipher in a very short time frame of less than a minute. Interesting to note we did not get a TCAS T/A or R/A. (enroute for the remainder of the trip TCAS seemed to be working properly). ATC then gave us instructions to fly heading 090 degrees and explained that he did not give us climb clearance from FL310 to FL350 and that he will be filing a complaint. Note: From the R/H observer's seat; through the cockpit speaker I heard ATC say FL390 was not available; climb and maintain FL350. [Relief] F/O read back to ATC; 'climb level 350;' [flying] F/O initiated the MCP climb procedure and we began a climb to FL350. After the events we notified Dispatch through ACARS. I called Chief Pilot and Director of Safety for notification.
B747-400 Captain reported an airborne conflict and wake turbulence encounter resulted from miscommunication between the flight crew and Delhi ATC.