Let me be the first to ask the obvious questions...
What time do you want to travel? When do you want to come back? Are you prepared to commit to certain trains or do you need to be flexible?
As the request is for the
cheapest RTN fare, I am
assuming Advance Singles are no use and that the passenger can travel off-peak.
Although details of the cheapest fare have been provided, it may be possible to buy a combination of tickets that may be cheaper than the through fare, in accordance with Condition 19 of the Conditions of Carriage.
If the request is in fact for the
cheapest combination of tickets, then as always, I'll bow out of that on the basis that I cannot be confident of answering that accurately (and it can be very time consuming to figure this out), but I would suggest using a site like brfares.com to research splitting the journey into a combination of tickets as that may save money. MSE's
Tickety Split only offers splits on single journeys but it can give an idea on where a split may work for a return.
However if the OP does some research, presents his findings so far, and would like some further help, I'd be very happy to help at that point.