Tony.
The Halfords report is inadequate in that is performing a simple voltage test under a meagre load. What is needed is a deep discharge test which simulates the heavy load of about 200 amps imposed by the starter motor, rather than the dozen or so amps used by the lights and screen heater.
Halfords are also wrong in their comments about battery coding. To my certain knowledge A3s from at least 2007 need to have the battery coded in order for the car's electronics to work correctly. It is even possible, though I am less sure of this point, that your repeated disconnection of the battery is causing the coding to be lost. It would need somebody more knowledgable than me to clarify that.
Whatever the cause of the problem, the symptoms you presented of the battery being unable to hold a charge are classic properties of a faulty battery, hence my conclusion that you need a new one. I suggest you get the car tested by somebody more competant than the clowns at Halfords. If and when you get a new battery get a decent one, have it coded, and never disconnect it without good cause.