Hi All,
First post here but felt compelled to do so after finding the forum through a search related to this problem, which until recently I also experienced. So I thought it might be worth mentioning what was identified and fixed in my case.
I have a 2016 XF S 3.0 D, which began making exactly the same noise as that in the recording last month. I took a jaguar technician out for a test drive in it and typically the noise didn't occur once, despite having been there for 7 days in a row up until then!
Credit to Jaguar however (Marshall's Peterborough in this case) as they didn't give up; I left the car with them for a couple of days so they could test and try and find it for themselves. When they did, despite being puzzled, they sent their own recording to Jaguar and received an immediate response that it was a known fault and a specific process of how to fix it. Whilst I don't know the exact detail, I am told it was an 'earth lead' and sure enough, a week after getting the car back the noise has gone and it's been fine ever since.
Hope this possibly helps anyone in the future who encounters the same issue - seems Jaguar are very much in the know about it, even if all the actual dealerships aren't!