I have fitted a Mini heater box, but adapted it to use the Minor controls, as the Mini ones are very different. The whole assembly is in a 1958 car, complete with the later type parcel tray.
From a thermal efficiency perspective, this is a pumped system, with very little height change, so the direction of flow through the heater matrix is immaterial.
Looking at the BMC Workshop Manual, it looks like whichever hose goes through the top hole through the bulkhead, goes to the top connection on the heater, and likewise for the bottom hole. This means on earlier cars where the heater return hose goes into the bottom of the radiator, the hose from the back of the head will go to the top of the heater matrix, but on later cars (shown in the picture below) it will be the return hose that goes to the top heater connection. Please see the extract from the manual below.

- Heater Upgrade Fixing Pt 1.jpg (857.46 KiB) Viewed 777 times

- Heater Upgrade Fixing Pt 2.jpg (1.39 MiB) Viewed 777 times