Go with Dulux Slow Living. At ΔE 2.3 from Farrow & Ball Purbeck Stone, it's a very close match — close enough that on the wall, in normal light, you'd struggle to tell them apart. Dulux Knotted Twine is right behind it at ΔE 2.4, also very close, just a touch lighter at LRV 55 against Slow Living's 52.6.
Anything under ΔE 2.5 is what the trade calls a very close match, so both of these are genuinely good. The difference between them comes down to that small LRV gap — Knotted Twine bounces back a little more light, which can matter in a darker room or a north-facing space where every bit of brightness counts. In a well-lit south-facing room, Slow Living's marginally deeper, more grounded feel reads closer to the original Purbeck Stone character.
Now, the honest caveat: Purbeck Stone is one of those Farrow & Ball greys with real depth and a complex undertone, and part of what people love is the way it shifts through the day — softly warm in some lights, cooler and greyer in others. Dulux matches the colour value well, but you may not get the exact same chameleon quality. That's true of any cross-brand match, not a fault of Dulux specifically.
My advice, mate: don't buy three litres off the back of a ΔE figure. Get a tester pot of Slow Living, paint a decent A2 patch — or better, paint a bit of lining paper you can move around the room — and live with it for a couple of days across morning, afternoon and evening light. If it leans a hair too flat for you, swap to Knotted Twine for that extra lift. One of the two will land it.
And whichever you pick, match the finish to the job: matt emulsion for ceilings and low-traffic walls, a wipeable finish for hallways and kitchens.