So here is the story on madder dye. I tried assorted net searches and got nowhere as regards local suppliers. This info came from a supplier whose upload inquiry form I was unable to complete for some odd reason. If you think you are going to find "madder sellers" in a net searcdh, don't. Unless, of course, there is time to do a lot of weird reading on yarns, dye history, etc. Ebay had not the dye so much as dyed yarns. Anyway:

"...the root contains rubian, rubiadin, ruberythric acid, purpurin, tannin, sugar and especially alizarin. Pseudopurpurin yields the orange dye and xanthopurpurin the yellow. The astringent taste, slight color and red color, are imparted to water or alcohol.

The most interesting of the coloring substances is the alizarin, and this is now termed dihydroscyanthraquinone. This occurs as orange-red crystals , almost insoluble in water, but readily soluble in alcohol, ether, the fixed oils and alkaline solutions. The alcoholic and aqueous solutions are rose-colored, the ethereal, golden-yellow, the alkaline, violet and blue when concentrated, but violet red when sufficiently diluted. A beautiful rose-colored lake is produced by precipitating a mixture of the solutions of alizarin and alum.

Alazarin was recognized by Graebe and Liebermann, in 1868, as a derivative of anthracene - a hydrocarbon contained in coal tar, and in the same way they elaborated a method for preparing it commercially from anthracene. Upon this arose rapidly a great chemical industry, and the cultivation of madder has, of course, decreased correspondingly until it may be said the coal tar products have entirely displaced the natural ones"

Note that alcohol, oils of an unspecified type, ether or alkaline solutions dissolve alizarin (also known as dihydrocyanthraquinone) which are the red-orange crystals and make them useable for dye purposes in that color range.

I don't know what they mean by alkaline solutions but this might be something from the process of leaching ashes to produce soap ingredients. This is basically lye. Though oils of whatever type in the 19th century are likely to be determined by reading about gunstocks, the readily available solution for alizarin is likely thinned lye. If "alcohol" means the stuff one could drink no proper Englishman would use it for that purpose unless for a special client who would be told of the use of his favorite gin in the mysterious mix.

The main issue is to find madder. A large art school or university or an art museum with classes is likely your best bet as the net offers confusion. This is not exactly a common bulk home maintenence product.