Apples will store if wrapped in tissue and placed in a drawer or two a cold room. Alternatively put them in an "Apple box" (get one from your local Tesco, they only throw them away) and put them in the loft where it is dark and cool. They should last several weeks. My Grandfather used to do this with his fruit crop and we would be eating them well into the new year. Much, I gather, depends on the type of apple but given that my lot can eat their way through at least 5 lbs a week they wouldn't last long here.
When we had apple and pear trees at the last house we kept some for eating in the manner described above and preserved the rest. If nothing else chop and core them and freeze them in pie filling sized bags. Apple pies throughout the winter.