Have you tried getting a bottle of the RedEX pro stuff? The gold bottle at Halfords. May be worth a shot first? Sling the bottle in with say 1/4 of a tank (25litres left ish)so it’s at a high concentration. Then give it the old Italian tune up down a duel carriage way for 40 mins. That should knock quite a bit of crud off the injectors.

Obviously other makes are avalible Heard good things about Seafoam but that seems to Be for petrol guys who arent having to deal with thick soot,carbon and general filth diesels seem To produce!

May be worth it before fighting with car taking it to bits!

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E53 3.0d Sport 119,000 Miles
E61 535d Estate - Hybrid turbos and Dark-side intercooler...389hp,792nm