Amazingly, I've had a second reply.

This time it's from the son of the man who, early in the Second World War, converted the car into a breakdown truck (A friend spotted the article in the newspaper, then gave it to him a few days ago).
Apparently his father, who owned the garage, needed a prestige car to use as a taxi and bought the Sunbeam for that purpose. This would have been in the late thirties.
The conversion to breakdown truck happened early in the war as they needed one and couldn't get one (for obvious reasons!)
Now that I know the car was in Walsham-le-Willows for quite a long time, and as a taxi, not just as a tow truck, I have contacted the Walsham-le-Willows history society to see if they have any photos I could look through. It might have been used for weddings etc. etc.
Alan