For those interested in this story...
On another site, more active on the topic (Ma BMW)
I learned that this is a common problem in many parts of Europe.
The animal seems to be a weasel rather than a rat.
It seems to like cables, tubing and soundproofing materials in most cars, BUT, only the soundproofing materials in BMWs - that's a good thing (all is relative).
The cost to replace the soundproofing under the bonnet in an Active Tourer is about €100.
There exists a weasel repellent ... but it doesn't seem to work.
Most people with this problem seem to just remove the half-eaten soundproofing and it doesn't seem to make an audible difference - just looks cheap and tacky.
Not a great finding... but, I suppose I'll have to live with it.