That the engine cut as soon as you disconnected the charger could indicate a faulty alternator. Once the engine is running the alternator should provide enough charge to keep it going. I presume the cat started OK for your trip to Sainsburys. Put the battery on charge overnight and try to start the engine in the morning. If it starts OK check the battery voltage with the engine running about 1500 rpm, and again with the engine off. The battery volts with the engine running should be about 14 volts and 12 when not being charged.
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