Anglicans will agree that we do not go immediately to heaven or hell. As we are a Creedal church, we believe in the Second Coming, Resurrection, and Judgment as stated in the Nicene Creed.
We will descend to the dead, just as Jesus Himself did. And, just as Jesus Himself did, we will be raised from death in the Resurrection at the Second Coming to be Judged.
Our continued regeneration will continue while awaiting for said "Last Day," so there is definitely a purification aspect to this period of waiting.
What many of us will disagree with is that, once we have finished our purification, we go immediately to heaven. We continue to wait, for our purification can only be finished once Jesus Himself declares us pure, not just by a particular judgment. Only the True Judge can declare us truly fit for heaven or hell.
In all other aspects, then yes; we Anglicans do believe in "Purgatory." The name itself does suggest a primary function of the place souls go to upon death, so it isn't an inaccurate name for it. Personally though, I call it "Sheol," which is its ancient name.