OK if you're planning to eat fairly soon, but not if you're planning to store. The bruising as they hit the ground is enough to cause rot during storage.

Cox is supposed to be ready for harvest in early to mid Oct, so even in a good summer beginning of September is a bit early. Its eating season is late Oct to Jan. I was always brought up with that thing about rattling the pips to see when it was ripe, but recently there's been some doubt cast on that.

I usually pick when the tree in question is starting to shed good apples as windfalls (I ignore the first few windfalls which are usually unripe fruit which have been attacked by blackbirds). Harry's right with his implication that not all the apples on the tree are ripe at the same time, so if your tree is small enough, it's sensible to do the gentle lifting thing - ie gently lift the apple and it should fall off, without any need for twisting. Only resort to twisting if you're trying to pick late apples before the frost, and expecting them to continue ripening in store.