1.8 Tdci starting issue

[Gsk2000uk]

Good morning I have a 53 plate focus 1.8 tdci. I baught this after the last owner got fed up when the turbo unit destroyed it's self. I've changed the turbo and given it a full service Inc glowplugs but it has still got a problem when cold. When you start the car in the morning it sound and fires but if I don't hold the revs to over 1k it dies and you can here it's running lumpy as soon as the engine warms up it  runs perfect  and you can here the desiel know quieten right down. There no fault codes showing and the glow plugs were changed to good Bosch ones with a new relay also the started spins nice as well.

Any help would be appreciated 

[Luke4efc]

Rough idle when cold is usually due to a cylinder imbalance. So stuff like injector wear (I'd say this is the most likely culprit), cylinder wear, worn piston rings, cylinder head valve wear etc.

I take it you've done the air and fuel filters? There's also the MAF to look at (I'm not actually sure if your car will have one). Compression test could be a good place to start without spending much money. At least then you can probably rule out ring/cylinder wear and head valves.