About the British Warm
The British Warm is a heavy double-breasted overcoat made from Melton wool, a tight, water repellent cloth with a raised nap. Aptly named, the coat is like wrapping yourself in a crackling log fire on a cold winter's day. (This reminds me of the time I saw a man walking down the high street of Bath carrying a bag of hot coals in his arms — not the most sensible way to keep warm. I think he was puddled.)
The traditional style of the British Warm is in a taupe colour with generous (generally peak) lapels for pulling up and around your neck if need be, and — like countless British classics — it has its roots in the British Armed Forces. The coat was introduced to the British military as an alternative to the officer's greatcoat around the time of the First World War.
Churchill was fond of the British Warm, and Prince Charles has been known to wear one. Perhaps the most habitual wearer of a belted version was Field Marshal Alan Francis Brooke (1st Viscount Alanbrooke) — based entirely on the number of photographs I've seen with him wearing it.
New and Lingwood
Word on the (well-dressed) street has it that New and Lingwood do one of the better variations of the British Warm (top and below).
You don't have epaulettes and a belt (though it has a half-belt at the back), but you have the six-button double-breasted style, gauntlet cuffs and — most importantly — the coat is made from Fox Brother's original 30oz Churchill British Warm overcoating cloth.