The way that prices change suggests that they are controlled by a computer.
On more than one occasion, we have decided upon the dates we intend to travel and checked the train times and costs accordingly. Then, for domestic reasons we need to make some arrangements which mean that we aren't able to make the actual booking before the domestic arrangements are confirmed.
In the delay that this involves ( a day or so ), I keep a regular check on the prices and it is evident that, for an any particular departure time, prices increase in direct relationship to the number of vacancies still available and not the days left before departure.
So if you are travelling at an 'unpopular' time ( midweek - early or late ), the price is less likely to increase than would be the case at a more 'popular' ( convenient ) time.
So if you want a convenient crossing time, the sooner you book the better.