The sensor you are refering to is a MAF (air mass) and the right one doesn't see any air flow until the 2nd turbo comes in at 2400rpm. 2012 TDV8 Vogue (L322)

Thanks to all the guys that contributed to this thread, I just cleaned the MAP sensor as per the advice here. As a side note - on the screenshots it does not get clear how big is this little , and it is quite small - less than a centimeter. Cleaned it with break cleaner.
I cannot tell if that gives any difference as I have issues with DPF and that was my first step in the troubleshooting process.
On the photos, cleaned, dirty, and the little black hole to the intake that appears to be quite dirty as well. That is probably my next step

Click image to enlarge

Click image to enlarge

Click image to enlarge

The workshop manual tells you to "clear the powertrain control module (PCM) adaptions" when replacing the MAF or MAP sensors. Is that still necessary when you are just cleaning them? 2012 Vogue 4.4 TDV8 automatic (LHD), Santorini Black
2008 Vogue 3.6 TDV8 automatic (LHD), Java Black

Do you have a diagnostic tool that can do it?
I used to clean mine's MAP sensor regularly prior to having EGR disabled, but just liked the revitalised performance after cleaning.

I have the IID tool. Just wondered if it's necessary. 2012 Vogue 4.4 TDV8 automatic (LHD), Santorini Black
2008 Vogue 3.6 TDV8 automatic (LHD), Java Black

do we know any reasonablely cheap replacements for the MAP?

i know some cars are really fussy about which sensors you use. Its actually a sport

Not anymore, 4.4 TDV8 now