Hale Navy is one of Benjamin Moore's most-loved colours — a deep, slightly soft navy that reads almost black in low light but opens up to proper blue in the sun. The trouble is the price tag and the faff of sourcing BM in the UK. Good news: there's a near-identical alternative for less.
COAT 2AM is your best bet. It lands at ΔE 1.9 from Hale Navy, which is well inside the "very close" range — most people couldn't tell the two apart on a wall, even side by side. With an LRV of 6.3 it sits at the same depth as the original, so it'll behave the same way through the day. COAT's paint is also a cracking modern formulation — low odour, washable, and self-priming over most surfaces.
If you'd rather stick to the big trade names, Crown Midnight Navy (LRV 6.6, ΔE 3.2) is a solid match and easy to get tinted at most merchants. Dulux Sapphire Splendour (LRV 5.3, ΔE 3) is fractionally darker but still in the same family. Both are a touch further from the original than the COAT — at ΔE 3 you'd notice a small shift if you held a Hale Navy card right next to it, but on a finished wall nobody's clocking that.
The "but what about" here: don't trust an on-screen swatch for a navy this deep. Navies are notorious for pulling purple or green depending on your light and what's next to them. Get a sample pot of whichever you fancy, paint two coats on a bit of lining paper, and tape it up on the wall you're doing. Look at it morning, midday and under artificial light.
For north-facing rooms, navy this dark can feel cold and heavy, so pair it with warm woodwork and plenty of light bouncing in. South-facing, it'll sing. Eggshell for woodwork, matt emulsion for walls — and two coats minimum over a grey primer for full depth.