For a short cut to change the background colour on a BBC Micro, type VDU 19, followed by a carriage return. Then hold down any numeric key until the background colour has changed, e.g. 1 for red, 2 for green, and so on.
It works in every mode except modes 1, 2 and 7. For flashing colours beyond 9, use VDU 19,0, in place of VDU 19.