Thanks for your comments.
These prompted me to research hum loops.
However I've had no success to date using the information so gained to this application.
I haven't tried using the chip +ive and _ive terminals to power the booster amp for fear of overloading the chip. I think the amp would need a greater current and voltage than the Bachmann chip could provide. After all it was intended for the smaller scales, IMHO the crux of the problem.
Attached is a simplified diagram of the system.
I've pretty much resolved to use 10 rechargeable low self discharge AA cells to power the booster amp. It works O.K with a 9V PP3 type battery but I can't imagine that working for long without needing to be recharged.