Of the alternatives I can point you at, Dulux Olive Grove (LRV 8.1) is the one to go for — it sits at ΔE 5.6 from Little Greene's Olive Colour. That's a noticeable difference if you held swatches side by side, but in a real room, on real walls, under changing light, most people wouldn't clock it. For a budget swap it's the sensible choice.
The other options drift further. COAT King Kev (LRV 10.5) lands at ΔE 9.2 — lighter and a touch fresher, so it reads as a different colour rather than a stand-in. Crown Racing Green (LRV 6.2) is right out at ΔE 13.9; that's a properly different green, much deeper and bluer, so don't think of it as a match at all.
Here's the honest bit, though. Olive Colour is one of those Little Greene shades that earns its keep — it's got a complex, slightly dirty, historical green character that doesn't photograph or sample-match cleanly. A ΔE of 5.6 captures the hue but not always the *soul* of it. On a feature wall or a whole room where the colour is doing the heavy lifting, the difference in pigment richness tends to show.
So my advice splits two ways. If Olive Colour is a supporting player — a hallway, a small utility, a cupboard interior — go with Dulux Olive Grove and pocket the saving. If it's the star of the room and the reason you fell for the scheme, spend the extra on the genuine Little Greene. Their Intelligent Matt and Absolute Matt hold that depth beautifully and you'll not regret it.
Whatever you land on, buy a tester and paint two coats on a bit of lining paper, then move it round the room across the day. Greens are the most light-sensitive family there is, and a north-facing wall will pull any of these cooler and greyer than a south-facing one. Sorted.