The speedo gets a pulse off the trans and obviously working. The odometer is gear driven within the unit and not engaged If your trip odometer is not working, failure is increased when trying to set it when the car is in motion.
It's called the odometer and there is a little plastic gear in it that breaks, this is always the fault when the speedometer part works but the odometer doesn't. There are vendors on Ebay that sell this gear, it is that common of a failure. Search for "smiths speedo gear bentley eight" and it will come right up.