I have a Redsleeves apple tree that grows well, is very vigorous and healthy. It tends to bear quite a lot of fruit too. However, every year the apples start to fall very early. At that point I start picking them, at least those that come off the tree easily. The down side with such an early apple seems to be that the fruit is still very tart. With later apples, they continue to ripen off the tree. However, with these they don't seem to ripen once picked.
This year I tried some very aggressive thinning of the fruit in June. It seems to have resulted in some good sized apples, but they are still falling pretty early. One good thing though - the first one I ate today was actually not too tart to eat. It could definitely have been sweeter, but it was edible and with a very good texture.
So if this is the natural time for the start of the apples in the garden, I could have a nearly year round supply if the Annie Elizabeth cookers keep right through to June as claimed in some of the books.
A number of the fruit do have signs of codling moth as usual. I've been picking the ones that I've spotted with holes in early, but now I will pick them and use for freezing, drying or some other kind of preserving I think.