The odd thing is, while the motor runs OK with NiMh cells,
it [sic] cuts out if the charger is plugged in -- that doesn't
happen with NiMh cells fitted.

I'm a bit confused as to what the /exact/ problem is. Could you
clarify? What exactly is "it" that cuts out? The charging? The motor?

The motor cuts out.

Thanks.

That's got me scratching my head. Why should the battery type have any
effect whatsoever on whether the charger powers the motor?

Does the motor run when no battery is installed?