Heads up for anyone with smoking, on secondary turbo activation 4.4 tdv8.
Car in question does NOT have the modified dual outlet secondary turbo drain but has been perfect for the 80000 miles or so of our ownership. About a month ago, while accelerating away from a junction, the car produced a smoke screen that Michael Knight would have been proud of. My initial thoughts were that our luck had run out and it was time for the drain mod. The symptoms were that the first acceleration of the day, above 2k rpm, would produce masses of dense smoke. Only seemed to be the first couple of enthusiastic accelerations then would be fine for the rest of the trip.
Upon doing more reading about the drain mod I had a look at topix with regard to the dual sequential turbo set up on the TDV8. I came across this line:-

" An air feed pipe, from the charge air pipe into the throttle assembly, supplies compressed air between the seals of the secondary
turbocharger compressor stage to prevent oil leaking into the compressor housing when the turbocharger is not running."

I had not seen anything about this in any of the discussions about this issue I had read, and I have read a lot!!! Anyway not hoping for much I checked this pipe on the car. What I found was a split about 10mm long at the back of the pipe. I cut off the damaged section and reattached the pipe to the throttle body. Since doing this over a week ago the smoke screen problem is completely solved!! Everything is back to normal and, despite trying to provoke the issue, the car has steadfastly refused to produce any smoke.
The pipe assembly I'm talking about is part no. LR033339, picture attached, it's the light grey pipe in the image connected to the throttle body.
Anyway it would be worth checking if these symptoms happen to you as it's a much easier fix than the drain mod. Not saying it is a solution for everyone but definitely worth a look.

Click image to enlarge

Nice one. I’ve not seen any discussion about that either, but very much worth checking.

 2011 Range Rover Vogue SE 4.4 TDV8

Previous cars :
2003 Range Rover Vogue TD6
1999 Discovery Td5 ES
1995 BMW M5 3.8 6 speed
1992 Range Rover 3.9 Efi Vogue
1992 BMW M5 3.8
1988 BMW 735i SE
1989 Ford Sierra XR4x4 2.9i
1981 Ford Fiesta Supersport

Did you buy the part LR033339 - approx £90 quid, and change it all over, what is in the photo below

No, the split was in the grey hose in the bottom left of the picture you just posted. This corresponds to the light grey pipe attached to the throttle body pipe in the photo I posted. The split was right next to the attachment spigot on the throttle body pipe and I was able to simply shorten the pipe enough to remove the damage. I probably will purchase the complete assembly but that will just be for me to "keep things correct" if you know what I mean.

It seems that this part is no longer manufactured or obtainable.

Also there seems to be two variants of these, one with the yellow or white thing in the middle of rubber hose and one without. Could you tell me if that "thing" is filter or one-way valve?

I assume, it is one way valve so when there is some boost, the boost will keep pressure on the secondary turbo to help oil seals sealing and valve will keep that pressure inside it.

If that's the case, then I could assume the one with valve is upgraded part and will help to reduce the leaking of secondary turbo.

Mine is a 2011 and is a different setup than yours.
Mine has a 90 degree rubber bend that goes direct to a steel tube.
Seems strange.