I suspect the validity on an Anytime Single is two days because of the 'overnight stay' rule - that is, if you start your journey on 27 October but cannot complete it that day (e.g. because you run out of trains), you are allowed to resume your journey the following morning before a certain time.
From the ticket terms and conditions:"Break of journey for an overnight stay is allowed. Where a journey continues into the next day, travel must resume before 1200 and no further break of journey is allowed except to change trains."
Some discussion about this recent change on railforums, http://www.railforums.co.uk/showthread.php?t=52268 and other threads
Some discussion about this on railforums, particualrly http://www.railforums.co.uk/showthread.php?t=52268 and other threads