So my car makes this unpleasant noise on cold start:
It's essentially inaudible if the bonnet is shut, and I haven't heard it in-cabin, so I'm not sure how long it's been there.

It does sound an awful lot like this:
However, that's a 4.0 car, and I was under the impression that 4.2 cars should have any tensioner issues?

 

Sorry that I can only be of limited help.
Video1 does not sound like video2.
In video2 you can hear the timing chain get some tension after a few seconds and it quietens down.
Your remains continuous.

 

That is a good point, thanks! I actually took the video several minutes after starting the car, as I noticed the sound while adding washer fluid.

However; there was no such noise when I started the car this morning and listened to it for a minute or so...

 

To me it sounds identical to a massive vacuum leak.
I can make my Toyota V6 sound like that by removing the oil filler cap.

 

Video #1 is fuel injectors firing. It's noticeable on the N/A cars due to the plastic intake.

 

Ranch this is a 4.2. And the OP says sound goes away

 

Yeah, 4.2's and 3.9's like what was in my LS. Sometimes they were quiet, sometimes pretty obnoxious. The N/A 3.9 valve train sounded like a sewing machine when wound past 6k. Sometimes my //R does at high RPM and sometimes not. Often wonder if it's the blower making noise or the valve train.

 

Hmm, what I mean is the "tsk-tsk-tsk-tsk" sort of chattering/ticking noise. I would assume a vacuum leak would make more of a hiss? Wouldn't a leak result in a fault code of some sort?

 

Pull your engine cover off and use a long screwdriver or wooden dowel placed against the base of your skull next to your ears as a stethoscope while you probe around the injectors. You'll find your noise.

 

Vacuum leak will be a hiss, but the net result of that leak will be improper running condition and noise.
I think I heard a hiss towards the end of the video.
I could be totally wrong.

BTW all our guesses could be wrong if the car has not thrown a code.

 

I passed the video on to a JLR tech friend of mine, his diagnosis was a failing VVT carrier.

You really want to get it looked at ASAP.

 

Thank you all. Just as I wrote earlier, the sound has yet to reappear, and I've opened the bonnet & listened on practically every start since then.
There are no fault codes, either. A moment ago I started the engine with the bonnet open, camera on tripod pointed at the engine to record any sounds, while I read codes with my i930; no codes, no weird sounds.

Cambo, I appreciate the diagnosis, but if it were the VVT carrier, wouldn't it make noise on every start, if not all the time?

 

What engine oil have you been using ?

 

"Liqui Moly Special TEC F 5W-30" it would seem, last changed 6 months ago.

The sound reappeared on the day before yesterday, when it was again sub-zero outside. It was very faint, but I noticed it when driving at a low speed, and only when on throttle even slightly. I stopped to listen about 5 minutes after startup, and it was audible just as it was before. I drove to work and the sound still remained as I parked, so engine warming up does not appear to affect it.
I park in an underground garage (15°C/59°F), and as I somewhat already expected, the sound was gone when I started the car as I was leaving work. It hasn't appeared again, but temperature dropped rapidly today so I fully expect to hear it tomorrow morning.

I've also paid more attention to the hiss Q&C pointed out; it's very audible, but I'm no mechanic so I'm trying to book a time for it to get looked at...

 

My son's '14 Jeep has a recall for belt tensioners that are noisy in cold temps. Perhaps...

 

I would recreate this situation again before going to the mechanic so that you can give him some concrete evidence as to under what conditions the noise happens.
In other words eliminate the fluke. Because sometimes mechanics do more than necessary because customer gave them incorrect clues.

 

Perhaps, as clearly the engine warming up has no effect on it. I took the long way to work this morning and used manual shifting to stay at around 2000 rpm while cruising to build up more heat, to no avail.

It's cold this morning, -10°C/14°F, and the noise reappeared. Curiously however, as I started the car, got out & opened the bonnet, the noise wasn't there; it only appeared perhaps 10-15 seconds after starting the engine.

I guess the best course of action would indeed be to look at the forecasts and take the car in to get checked on a cold morning.

 

Well, the noise reappeared on a few cold enough days, but on the days I had the time to take the car to get looked at, it wasn't as cold.

The hissing was checked out however, but in the end they concluded that they could find no leaks. They also had a 4.2 X350 in, and said they started it up and it made the same hissing noise. Thus, I'll just accept that it's normal.

I'm too paranoid for this stuff, maybe I should just always listen to music while driving.

 

My old X350 always made a hissing sound that could only be heard with the bonnet up. I remember learning somewhere that it was the PCV system that hissed but who knows for sure.