If the ticket is shown as being an "Advance" ticket, then it will only be available up to the day before travel, online or at the station. The advance fare becomes more expensive closer to the date of travel ie. had your booked an advance fare 2-3 months ago it would be cheaper than it is now. In short if the fare is shown as "Advance" it will not be available on the day of travel.
If however the fare is shown as being a (Super) Off-peak/anytime (day) return/single it will be available on the day (unless there is a web discount applied. Depending on which website you are using, it may be shown with a red asterisk if it has a web discount applied.)
EDIT: Looking at available fares, I presume you mean the £26.75 day return fare using a family railcard. If so, this is indeed a "walk-on" fare, and should be available to purchase on the day. However, if you are willing to tie yourselves to a particular train which you would
have to get (ie. the ticket is not valid on other services) it is possible to get it down to between £22.90 and £25.00 depending on what train you catch using "Advance" fares, (ie. only available to buy today) by clicking the "2 singles from £22.90" tab on
this page, and selecting the trains you wish to catch. However if you want flexibility, stick with the £26.75 fare.