You're correct, the Brits had captured Antwerp but it was unusable becasue they didn't clear the approaches.
Based upon the timelines, I'll have to disagree with both of you. Antwerp fell about 10 days before Market Garden was launched. If you look at the British progress along the coast, they were not slowed down by resources being diverted to MG. (Also look at the relatively short timeline between MG approval and implementation.)
So the capture of Antwerp wasn't delayed by MG; neither was the clearing of the port.
Neither the armor of XXX Corps or the Airborne troops would have been likely candidates for manpower to re-open the port. Naval units would have to work on clearing the harbor itself which, along with its approaches was heavily mined, and engineering units would have been needed to deal with on-shore issues. (Yes, some engineering units were assigned to XXX Corps, but not enough to make a difference at Antwerp.) The port was re-opened for shipping about 3 months after it was re-captured.