There maybe something vintage around those numbers but I don't think there's anything modern. Have you considered the Alpina bars?
or there's the Cinelli pista bars but they only go down to 40cm.
Failing that, maybe narrow compacts and a negative rise stem?
Nitto B123 are 170 drop and come in 34cm wide or more but you'll need a 25.4 stem or shim to 26mm.
If you can't find any in the UK ATM ( I could only find 38cm or greater with a quick look) then you might have to get direct from njs export
Expensive, but if that is no issue (and you can find them) you can get these in 37cm and 148mm drop:
There are plenty of Chinese 3t Scatto-alikes on the market at places like AliExpress. Same dims - 89mm reach, 148mm drop (for 36cm only, mind - narrower and that drop goes to 120mm). I got a second hand set for £50. Decent bars and really stiff.
Other than that, you're looking at Alpinas. They pop up regularly on the Facebook track classifieds group around the £100 mark.
If you don't mind a shim, I've got a set of 36cm Nitto B125s you can have (150mm drop)? Shim's superglued on and other than that they're only used once.
Nitto b 125 or Nitto b 127 - - you can get both narrower Or wider - check out track supermarket or alex cycles or bens they all got em
Does anyone know any handlebars for track use that are 36cm wide or less and are 140mm deep or more?
I am struggling to find any.