If you love Little Greene::Jack Black but not the price, the standout alternative is Dulux::Rich Black (LRV 2.4). It measures ΔE 2.1 from the original — under 2.5, which means very close indeed. On a wall, side by side, you'd be hard pushed to tell them apart, and you'll likely save a fair bit per tin, especially in trade sizes.
Why does Jack Black command its price? It's that soft, slightly blue-black depth Little Greene does so well — a black with body rather than a flat, dead black. Rich Black holds onto that character well enough that I'd happily spec it as the value swap, particularly across larger areas where the saving stacks up.
The other matches in the database are further off and I'd be honest about that. Crown::Rebel (LRV 4.1) comes in at ΔE 6.4, and COAT::David Rose (LRV 4.1) at ΔE 7.1. Both read noticeably lighter and shift in undertone — anything past ΔE 5 is a visible difference, not a dupe. They're decent blacks in their own right, but don't buy them expecting Jack Black.
The "but what about" here is finish. A near-perfect colour match in the wrong sheen will still look different. Jack Black in Little Greene's Intelligent Matt or Absolute Matt has a particular flatness — if you want Rich Black to feel like it, match the finish band, not just the hex. On woodwork and trim, go for an eggshell in both cases.
Practical advice: black is unforgiving, so always get a tester of Rich Black and brush it out generously next to a Jack Black sample on the actual wall, in daylight and at night. Two coats minimum over a grey or tinted primer — black goes on patchy over white, and you'll save yourself a third coat. Mate, get the prep right and Rich Black will do the job for less.