For the return journey we went to Canada Water and tried to use the replacement bus service. It was a shambles - poor signage, inconsistent announcements and when we eventually found a rail replacement bus, it was terminating at New Cross Gate, where a bus full of people was decanted onto the narrow and crowded pavement to wait for a second rail replacement bus (for the same line, remember).
Genuinely surprising given the generally high standard of service from the Overground, but I guess they don't have that much experience (yet) of running rail replacement buses.
The rail replacement buses which serve FH/HOP are operated on behalf of Southern by Go-Ahead London.
With the exception of one day over the festive period last year, it's Southern who are charge of the buses when the Overground is shut between NXG and West Croydon/Crystal Palace.
London Overground are responsible for rail replacement buses north of New Cross/Gate and on the South London Line to Clapham Junction.