I'm not usually lazy about research, which I enjoy, and I rarely find myself struggling to identify a prototype I'd like to tackle in either 'straight' or fictionalised form.
In the case of the Brighton, however, I find my enthusiasm for the company far out strips my meagre knowledge and I look at the web of green lines stretching out to the south of London in my pre-grouping atlas with a growing sense of confusion.
In short, I would be grateful for any suggestions for a suitable basis f
No, it's a local, according to the caption, passing beneath the GC bridge.
The NRM picture is apparently of the Sunny South Express, and is given as 1910. The stock looks older than in the J E Kite album Addison Road shot, where the service is, as you note, called the SS "Special", and which is captioned 1914: