I really do not think your problem is rooted in your battery based on the information you've given. If you've got clean connections, your starter is cranking reliably, and the engine is firing up (at least most of the time) but dying afterward.
I suspect your issue is either going to be with your coil (most likely), distributor, and/or spark plug wires.
It could also be possible that your fuel pump has begun to go bad and that it only runs for a very short period of time before cutting out. If the car is off and has not been started for a day or so you should be able to hear the pumps ticking if you turn the key to the run position but do not start the car. They will tick moderately quickly, progressively slowing as they fill up the float bowls in the carburettors, until they come to a stop. It is not at all uncommon for one of the two pumps in the dual SU setup to have stopped functioning completely and the owner not be aware of this. The car can run perfectly well on one of the two pumps, but then when that pump fails you're dead in the water. I had symptoms quite like yours and it turns out that one of the two pumps in my dual unit had been dead for years, rusted solid, and the other was giving out. The car would sometimes start and run for a while, others it would start and die after a short time. It all depended on how long the remaining pump would function normally before flaking out. Once I rebuilt both sides of the pump everything returned to normal. If you haven't checked your fuel pump this could be the culprit. If you have the car up on a lift you can have someone turn the key to the run position with your hands grasping both sides of the pump. See if you feel action in each half. Then they could start the car and you should keep feeling to see if the pump just gives out suddenly.
Not knowing where you're located and the chassis number of your car puts advice-givers at a disadvantage. Crewe had somewhat different designs for various systems depending on the market for which the individual cars were destined. They also had the habit of making mid-production changes when one part they'd been using was exhausted and the one they intended to replace it with was available.
If you have not visited the RROC-Australia Post-War Technical Library
, SY Cars Section, to view and download all of the workshop & parts manuals for your car, along with other technical service bulletins you really should. The RROC-Australia Tee-One Topics Archive
is also a treasure trove of helpful information. Also consider downloading the Rolls-Royce & Bentley Parts, Repair, Restoration & Other Resources Compilation