Agreed, all you need is a corps to mask Antwerp as you make your push south. It's really, really hard to take early, unless you don't plan on pushing into France. It requires a full army, and you'll take a LOT of casualties.
I usually pull my super heavy artillery out of the armies and attach them to the corps masking Antwerp, just because they are a PITA when you're trying to advance. If you get lucky, you can get a few breaches in the fort. Once your advance peters out, you can pull an army north and assault it a few times through the winter.
I haven't tried blockading it with the HSF, but that's another option to prevent the Brits reinforcing it. You won't really impact supply (even with Easy Supply off), because there's a larder in the fortress (and usually a supply wagon as well), so don't waste your time trying.