National Rail Enquiries offered a £20.80 fare each way. However, when I tried to buy the tickets I was directed South West Trains website and this did not acknowledge that these tickets at the quoted fares were available.
I tried to buy these tickets on two different days, two or three attempts were made each time with no success. Accordingly, I selected the tickets I required but declined South West Trains as the seller when this was offered and selected another ticket sales site. This recognised the existence of these advance single tickets at £20.80 each. I purchased them!
However, it does pose the question why does South West Trains not offer the cheapest tickets for journeys on their services and direct potential customers to tickets at up to three times the price.