Air carrier inbound to IAD; low on fuel and with three other company aircraft on the frequency with similar flight numbers; initiated a turn to the final; was corrected by ATC; controller stating turn was for company aircraft.

Narrative

After having received delay vectors twice enroute; and while my First Officer (pilot not flying) was calling inrange; I declared minimum fuel about twenty minutes from destination when the FMS indicated we'd land with 2100 pounds of fuel; 200 pounds above reserve. Upon checking in with the Approach Controller; we were advised by the controller that he'd turn our base in about two minutes. The approach environment was very busy; with instructions being issued about every three to five seconds. On frequency were Company ABCD; ABCE; and ABCF and many others. Less than two minutes after that (perhaps one to two minutes); the Approach Controller instructed us to turn right to 270 degrees. We complied; and though it was less than the two minutes previously indicated; it made sense in light of our previous minimum fuel declaration. A moment later; the Approach Controller urgently advised that he'd not instructed us to turn base and issued an immediate left turn; while calling out traffic on final. I pickled the autopilot and quickly rolled left to the assigned heading; then taking the radio for a moment; advised that we'd heard the instruction and read it back. Shortly afterward the Approach Controller turned us to our base heading; pointed out traffic to follow; and cleared us for the visual to Runway 1R. He also apologized for not catching our readback. I responded with 'no worries; we're over to Tower. Well; of course stressing due diligence on the radio is important; but taking measures to minimize similar call signs arriving in the same bank would help; though that might be impractical. A possible factor here could be controller experience. We don't know what the individual controller's task load or experience might have been; though as previously mentioned it was a very busy environment. We believe we heard our call sign; but only listening to the tape will bear that out. We think it's likely that he used our call sign intending to turn someone else; though it's possible that we BOTH misunderstood the callsign. In any case; the Approach Controller did a great job catching our being out of place; no matter who goofed and all I can think of to prevent recurrences is for us all to stress proper radio discipline.