Thank you for the extra information, that raises problems.
Very early BMC 1.5s had a two hole fixing inertia starter which has just a single larger cylinder body, I have only ever seen one in the 70s they were impossible to obtain, so that would be an overhaul or a new engine backplate, flywheel housing, engine mounts and possibly work on the engine beds and possibly a new flywheel.
Having scared you many of the "normal" 1.5s have a three hole fixing, but only held on by two bolts because of access problems. These moors consist of the larger "body" cylinder with a much smaller cylinder mounted on it. The small cylinder is the solenoid, and it will have at LEAST one thick battery cable, one thin "start signal" cable and thickish short black cable or a shaped copper bar joining one of the nut type solenoid terminals to the large cylinder. They are readily available, although you might end up with the solenoid differently orientated.
Now a warning for others, although this does not apply to all or perhaps the majority of BMC 1.5s. Nowadays NEVER hit the starter, modern ones have permanent magnets that shatter easily and if you shatter then you will be buying a new starter.
How did you ascertain the battery is fine? Just measuring the battery voltage means nothing. We need the battery voltage while you are trying to start, it should be over 12V., but other problems in the circuits can give a satisfactory voltage, but the stater still only click.
If it is an OVAL two hole mounting bracket then you need to get it to someone to overhaul it, or, drastic as it may seem. prepare for major expense for an engine change or major engine work.
I wonder if those two hole starters were actually off the B series petrol engine so things like Austin A50s and Morris Oxfords.
Can you post a photo of the starter, the white "discharge", the starter wiring and the back of the engine.
Put the motor back and connect, then measure the cranking voltage at the battery and then between the thick black lead terminal on the starter and any clean metal or battery negative and post them here. That way we can try to eliminate anything other than a starter fault.
If it really is a two bolt starter then instead of hitting it with a hammer you should see a little square stuck out the back of the motor. If you try to twist this with a spanner it will either turn, be it with resistance, or lock. If it locks try applying a bit of force in both directions. if it has jammed you will hopefully get a click as you wind the pinion away from the flywheel, and then it might start, but that indicates pinion or flywheel teeth damage on an inertia starter - maybe a photo of the pinion as well.
I am really hoping it is not a two hole inertia starter.