Wooden container with screw on top

I believe 47 Haymarket is a street address in London and Hairsine was chemist and or pharmacist. This page will give you some info https://londonstreetviews.wordpress.com/tag/chemist/
I found a stoneware jar on eBay with the Hairsine & Co 47 Haymarket mark https://www.ebay.co.uk/itm/Rare-Victorian-Two-Tone-Stoneware-Jar-Hairsi…
My guess is that your container carried some sort of chemical or pharmaceutical. That’s a start. If I find more info I’ll add to this.
This business seems to be related D.R. Harris & Co and it still sells shaving creams, soaps, skincare products and fragrance so maybe that’s what the chemistry was https://www.drharris.co.uk/
Another retailer selling D.R. Harris & Co today https://www.trouva.com/boutiques/dr-harris-and-co-ltd-in-sw1a1hb
I’m not finding any more info. The wooden containers or jars I have seen don’t have threads and so yours seems different that way. Also no way for me to guess a value. Let’s hope someone else knows more. And I don’t think bamboo, not sure the wood but believe turned on a lathe.

Mark pretty much covers the available information, there are tax records one can look up for business owners that would nail down a solid timeline, but pieces like this are not considered rare or that valuable. Most date from the early 1800's through the 1880's and were made of Fruitwoods, such as apple or pear because they were less prone to warping or cracking due to the dense grain structure.