Hello again,
Sorry for my delayed response but only remembered to ask the 'old chap' about this at New Year.
He tells me that, definitely during the late 40s, there was no signature tune, rider's parade etc. The riders just gave a wave as they came out for their first heats.
He remembers hearing "Marching Along Together" when the Rangers went to Wembley, as Wembley always had a parade, but feels almost certain that he never heard it at New Cross whilst he was there (46-53).
Pip