Buying advance train tickets in the UK

Usually buying your ticket in advance is cheaper but not always.  Before you buy a ticket, particularly if it’s for a day return, check to see what the price of the ticket is if you buy it on the day.  As I discovered the other week, buying a day return in advance actually disadvantaged me as you have to book a particular time for both journeys and even the return point was fixed, rather than the generic “london terminals”.