Hi
I walked the CF in November of last year, 27th Oct(SJPdP) to 27 Nov(SDC). Accommodation was perfect, places started to shut at the end of October, but there was enough staying open to not make it a problem. What you will find with your guidebook(
John Brierley) and the sheet from from the Pilgrim Office in SJPdP is that the details of places open is not 100% correct and vice versa for places indicated as shut, but this never really seemed to matter.
Like other posters have said dont worry about beds. I would never usually set off untill 8-9.30am, usually arrive late afternoon and there would always be something.
If you get good weather you wont believe your luck, it was still possible even in late November to lay in fields taking in the rays from quite a warm sun, have a snooze or watch the world go by.
Mike