CAC might swear by Trainline but there are also a great many people who swear
at Trainline.
I used to run a railway station and I got fed up of explaining to customers that the ticket that Trainline had sold them wasn't valid for travel, meaning that they'd have to purchase another ticket at the booking office. (For example they sold tickets to one couple using an offer that was only valid with operator A, on a train run by operator B. Further, they'd managed to allocate reserved seats despite the fact that operator B's trains didn't even have numbers on the seats, yet alone accept reservations for them!).
AVOID! AVOID! AVOID!
If you really must use a third-party website, use this one:
http://www.redspottedhanky.com/
However I've just tried the National Rail website and been quoted £10.50. Clicking 'Add to Basket', and then on 'Checkout', took me to the Southern website, where the same fare was offered.
Remember as well that you don't need to use the default ticket provider offered by the National Rail website. There's an option to let you choose a different provider in the blue 'Tickets' box underneath (and to the right of) the train times. For example, I can book that ticket via Abellio Greater Anglia or, indeed, with most other operators.