The line from Streatham Junction and Windmill Bridge Junction was quadrupled from 6 July 1903. The new platforms were on the east side. Thus what became known as the emergency spur had in fact been the original connection between the line to West Croydon and the line through Thornton Heath. The line through Selhurst was opened on 1 December 1862, though Stations were only at Thornton Heath (briefly Colliers Water Lane) and Streatham Common.
22 May 1865 was the day the chord between the West Croydon Line and Selhurst. The station itself had been opened on 1 May 1865.
My source is the very comprehensive Croydon’s Railways by MWG Skinner published in December 1985.
Of course the original railway between Wandsworth-ish and Croydon-ish ran via Streatham Hill (as can be seen from the straight track alignment from Balham to Streatham Hill vice the sharp curve towards Streatham Common).
You can see similar evidence of the original track alignment at stations on the newer route too. For example, Thornton Heath and Streatham Common in particular have much, much straighter alignments on the Fast line platforms. The curvature of the Down Slow platform at Thornton Heath is magnificent!
(However, the station buildings at both are in preference of the Down Slow side of the station. You can also see another unusual feature in that many BML platforms north of East Croydon are numbered the opposite way round to what you’d expect - Platform 4 is for Up Fast traffic and Platform 1 for Down Slow traffic. Platform 1 at other stations in the London commuter belt will usually be for express London-bound traffic, of course.)
Pedantic note, though... I think you mean Streatham North Junction (or perhaps Balham) and not Streatham Junction, as so far as I know, Streatham Junction has never had quadruple track on any of its routes.