Olive Colour from Little Greene is one of those greens that does its best work drenched — walls, woodwork and ceiling all in the one shade. It's a muddy, slightly khaki olive, and it wants warmth around it, not crisp brightness.
For your whites, go chalky and creamy. Farrow & Ball's Au Lait (LRV 80) is the one I'd reach for — a soft, milky off-white that sits beautifully against olive without fighting it. Paper III from Paint & Paper Library (LRV 75.3) is another cracking option if you want something a touch greyer but still warm. Steer well clear of bright, blue-white trim — it'll make the olive look dull and dirty rather than handsome.
For depth and contrast, Mylands Cigar BH.20 (LRV 11.8) is a proper rich tobacco brown that grounds the scheme — gorgeous on a feature joinery run, a bookcase or a lower wall in a two-tone setup. It picks up the earthy undertone in the olive and pulls the whole thing together.
When you want a lift — and olive does need one or it can go a bit flat — bring in an accent. Dulux Fuchsia Falls 2 (LRV 29.8) is the surprise here: a muted, dusky pink-mauve that plays off olive's natural complementary partner. It works brilliantly in a cushion, a throw or a single painted piece. If pink's not your thing, an ochre or burnt-orange textile does the same job — those warm spice tones are olive's natural mates.
Now the materials matter as much as the paint. Antique brass, aged bronze and smoked oak are what make this colour sing — chrome and cool greys will leave it looking sludgy.
Practical tip: drench the whole room, including the ceiling, then layer warmth back in with textiles and metals. A single accent wall in olive on cool white walls almost never works — it needs the full commitment to earn its keep.