When the car is cold (typically having been left overnight), it is absolutely fine. When it is up to temperature, it is absolutely fine. When it is neither, it idles extremely roughly to the extent that the car shakes. It is worse in Drive than in Park or Neutral. As soon as you apply power, it settles down.

I've had it to my specialist. The hoses are fine and there are no fault codes showing up. I don't want to start changing parts at random so I'd appreciate any thoughts, please.

2007 3.6TDV8 with 72000 miles. 2012 4.4 TDV8 Westminster
2007 3.6 TDV8 Vogue - gone!
2003 V8 HSE (LPG) - gone!
2018 F-Pace 25t Portfolio
1974 LR Series III Lightweight FFR
2014 BMW 640i Gran Coupe

what diesel you using mine used to have rough idle when cold on any fuel other than shell ultimate L322 2008 vogue
R53 Cooper S Works tuned beyond the works SOLD
R33 Nissan Skyline in rebuild 400bhp atw

Standard stuff (mainly Asda).

A few tanks of V-Power then? 2012 4.4 TDV8 Westminster
2007 3.6 TDV8 Vogue - gone!
2003 V8 HSE (LPG) - gone!
2018 F-Pace 25t Portfolio
1974 LR Series III Lightweight FFR
2014 BMW 640i Gran Coupe

try a tank of the good stuff it may solve it L322 2008 vogue
R53 Cooper S Works tuned beyond the works SOLD
R33 Nissan Skyline in rebuild 400bhp atw

check the live data and compare the readings from the left bank and the right, they should be pretty close to each other at all times

one reading being quite different (but not enough to ping up a code) could help you find the answer

could be a sticky EGR?

Good guess.

This had been ongoing for about a year with no fault codes and getting progressively worse. It finally threw one up.

It was nothing £1000 and two new EGRs wouldn't fix. In fairness, only one had failed but I had them both done while it was all apart. All now sorted. 2012 4.4 TDV8 Westminster
2007 3.6 TDV8 Vogue - gone!
2003 V8 HSE (LPG) - gone!
2018 F-Pace 25t Portfolio
1974 LR Series III Lightweight FFR
2014 BMW 640i Gran Coupe