Thank you for the above.

The very nice guy who did the diagnostics on the BCM has just wiped and re-set BCM, and so far, no alarm noises or light flashes.
So I will delay battery purchase.
If I come back very angry (not that I am ever angry), it will mean that the battery fix has failed, and Im still being disturbed during my very important shopping expeditions (!) by my Bull screaming and kicking out for no reason in the car park.

BTW - a sideline comment - how jolly easy is it to whip these X-fires round? WOW, even when trying to drive STRAIGHT enormous Fun! xxx