B747-400 Captain reported an air turn back after the aircraft failed to pressurize. MEL procedures were not followed regarding an out flow valve that was not locked out.

Narrative

'Upon departure from ZZZ we noticed a high cabin climb rate. We monitored the cabin altitude; but as we approached 10;000 feet it was clear the cabin was climbing with the airplane. We notified ATC and leveled off immediately. We got a Master Warning for Cabin Altitude and completed the QRH Checklist. We looked at the outflow valves and noticed that the right outflow valve (which was on MEL) was fully open and the left outflow valve (which was functioning normally) was fully closed.We again reviewed the DDG (Deferral Directions Guide) for the right outflow valve and realized that maintenance was supposed to have closed the right outflow valve manually on the ground per the MEL and they had failed to do so. We remained on the departure procedure except for maintaining 10;000 feet while we determined further course of action. We had about 60 tons of fuel to burn or dump before we would be able to land; if we needed to return to ZZZ. We called Dispatch and informed them of our situation. We asked them to patch in Maintenance; described what was going on and our belief that Maintenance hadn't completed their procedures on the ground per the MEL and asked them what their recommendation was.They concurred that Maintenance hadn't closed the valve on the ground per the MEL procedures and instructed us to close it manually. Following closing the valve manually the cabin altitude began to descend and aircraft appeared to pressurize normally. After a brief discussion with the rest of the cockpit crew; Maintenance and Dispatch; we decided it was safe to continue the flight rather than dump fuel and return to ZZZ.We asked Dispatch to do an inflight re-dispatch due to the extra fuel burn caused by remaining at 10;000 feet for approximately 20 minutes while we resolved this situation.Although I had elected; with dispatch concurrence; to add 2 extra tons of fuel for enroute turbulence; the combination of the extra fuel burn by leveling off at 10;000 feet and losing fuel the entire flight at a rate of approximately .2 tons/ hour ultimately resulted in not meeting our min fuel. Dispatch received approval to use a closer alternate to ZZZZ1 that was not normally authorized and we were able to continue on to ZZZZ1 and land as planned.Additionally we suspect the fuel flow numbers for Aircraft X may be inaccurate. The winds for most of the flight were more favorable than forecast; we had no enroute deviations; yet we lost fuel the entire flight and landed with almost 4 tons less fuel than planned using the IR from dispatch; 17.1 vs 20.8.Suggest Maintenance be more vigilant in the future to ensure they complete the procedures correctly for a maintenance deferral. More cooperation from ZZZ maintenance would also be helpful. I had to ask multiple times to get a briefing from ZZZ Maintenance and when it was given it was incomplete and the mechanic didn't seem to be familiar with either our deferrals or the status of the daily/ transit checks. Also suggest the company review the fuel flow numbers for Aircraft X to ensure accuracy.