I'm lucky enough to have had better weather than most of you poor souls but even my apples aren't much bigger than a golf ball yet.
If Hudson Belle is really inundated - and who are we to say otherwise - then I would suggest after making pies and puddings to make apple juice. I chop my glut of apples - skin and core included - and cook until really soft and mushy with just enough water to cover. Then scald an old pillowcase (which I use for the job) for 15 mins to kill any germs and then upend a chair on the kitchen table and attach the pillowcase to the four corners with string. Put a large clean pot under the pillowcase to catch the drips. Empty the apple into the pillowcase and cover everything to keep out flies. Go to bed - or out for the day if you do it in the morning. Anyway, just leave it alone.
In the morning you have a pan of beautiful apple juice. Don't be tempted to squeeze the pulp - you'll just get cloudy juice. Put the mush on the compost heap and reheat the juice to just boiling. You can add sugar to taste if you like at this time. Probably best to with just cookers but I don't usually add sugar as I use mixed apples. Pour the hot juice into hot sterlized bottles or jars and seal immediately. I use most of my juice to make jams as it is the best source for pectin. It will store really well.