There is a bit of confusion here.
If you book in advance you get the choice of buying an advance ticket (cheaper, but limit you to a specific train, and are not always available) or a walk up ticket (off peak or anytime depending on the time of your journey). If you buy advance tickets, you will buy two singles. If you buy a walk up ticket, then its nearly always cheaper to buy a return.
If you do not book in advance, you do not have the option of the advance ticket. Buy the walk up ticket will not be any more expensive than if you bought the walk up ticket in advance.
I would personally avoid the trainline as they charge a booking fee.