If you want Ammonite without the Farrow & Ball price tag, Dulux Gentle Moon and Dulux Thimble Case are your answers. Both sit at LRV 66.1 and come in at a ΔE of 1.3 from the original — anything under 2.5 is what we'd call very close, and under 1 is genuinely imperceptible to the eye. At 1.3 you're so far into the margin that nobody walking into the room would ever clock the difference.
The two Dulux colours are effectively interchangeable for this purpose — same LRV, same ΔE — so grab whichever your local stockist or trade counter has mixed and ready. Ammonite is that lovely soft warm grey that reads almost like a sophisticated putty in good light and pulls cooler when the light drops, and both Dulux options carry that same understated character.
Now, the honest bit: a near-perfect colour match doesn't mean a perfect finish match. Farrow & Ball's Estate Emulsion has a particular chalky, light-absorbing depth that comes from how the paint is formulated, not just the pigment. Dulux Diamond Matt or Heritage Matt will give you the colour bang on but with a slightly different surface quality — a touch more uniform, a touch more wipeable. For most people that's a feature, not a fault, especially in a hallway or a kids' room where you'll want to sponge off the odd scuff.
My advice: order a sample pot of Gentle Moon (or Thimble Case — coin toss), paint a decent A2 patch, and live with it across a full day. Warm greys like this shift more than people expect between morning and evening light, and you'll want to see it doing its thing before you commit a whole room. If it behaves, you've saved yourself a fair bit of money for a result no one will ever tell apart.