Dock Blue is a deep, muddy grey-green-blue, and the worst thing you can do to it is fight it with a crisp bright white. That sharp contrast bleaches out all the warmth and leaves it looking flat and cold. So the first rule: drench it. Take Dock Blue up the walls AND onto the woodwork, skirting and any panelling. Tonal, enveloping, gorgeous.
Once it's drenched, you lift it with warmth — not cool brilliance. The natural partners are smoked oak floors, antique or aged brass hardware, and a single warmer accent to make it sing.
For that accent, Dulux Copper Glow (LRV 30.1) is spot on — a soft burnt ochre that brings out the green undertone in Dock Blue and stops the whole scheme going gloomy. Use it sparingly: a chair, a lampshade, the inside of a cupboard. One warm note, not three.
If you want a softer, off-white companion for ceilings or a connecting hallway, go for Paint & Paper Library Sand I (LRV 95.4) rather than a clinical white. It's a barely-there warm neutral that reads as light without snapping coldly against the blue. Farrow & Ball All White (LRV 92) is the cleaner option if you genuinely want a fresher feel up top — but it's the more daring choice and only works if the rest of the scheme is warm enough to carry it.
For depth — say a fireplace, a media unit, or grounding the lower half of a two-tone wall — Mylands Cigar BH.20 (LRV 11.8) is a rich tobacco brown that pairs beautifully with Dock Blue's green register. Very handsome, very library-ish.
Practical tip: test Dock Blue in both daylight and lamplight before committing. It shifts noticeably — greener in cool north light, almost teal under warm bulbs. Get a decent sample patch up on two walls and live with it for a couple of days. Sorted.