There is no provision for this type of excess in the official procedures, so officially it is a new ticket, but it can't hurt to give it a go. East Coast ticket offices I heard are quite good at excessing away Railcard discounts, so perhaps Stevenage is a possibility for you.
Alternatively depending on the journey, it may also be possible to wait till departure and explain your circumstances to the guard. Since you have paid more than one full fare ticket, I cannot imagine many guards having an issue, but obviously this approach is not always possible, especially if you have gatelines at your origin station and/or you have multiple legs to your journey.