I have a side embossed A.J. White. The other side of mine reads: Curative Syrup. There's also and amber one that says Shaker Family Pills. I believe those are American bottles. He must have got around if yours is from London.
The medicine was made from herbs, roots and botanicals grown by the New York Mt. Lebanon Shaker community. One of the medicine was called Mother Seigel’s Curative Syrup and was packages by Andrew White.
Here is a little more history about the bottle.
"Recommended for dyspepsia and all diseases arising from deranged digestion"
Members of the United Society of Believers--the "Shakers"--have long been renowned for their skill in the preparation of various types of medicines. The Shaker community of Mount Lebanon, NY, established its first medical garden in 1820. By 1853, Mount Lebanon was producing 42,000 pounds of herbs, bark, and roots and 7,500 pounds of extracts.
In 1875 the Shakers of Mt. Lebanon, NY joined in a business deal with Andrew Judson White, a proprietary medicine maker in New York City. White agreed to buy all his botanical ingredients from the Mt. Lebanon community in exchange for a loan to revitalize his business. White was then able to capitalize on the Shaker reputation for high quality, pure drugs, and so distance his products from some of the shadier aspects of the "patent" medicine business. One of his earlier products, Mother Seigel's Curative Syrup, was renamed Shaker Extract of Roots and became one of the company's most popular medicines. Shaker Digestive Cordial was introduced at the end of the 19th Century.
"The Contra Constipation Pills," for a medicinal preparation for human use. A. J. White, Limited, 35, Parringdon Road, London, E.C., medicine manufacturers. 299,568.
"Mother Seigel's Curative Syrup," for a medicinal preparation for human use. A. J. White, Limited, 35, Farringdon Road, London, E.C., medicine manufacturers. 299,799.
"Mother Seigel's Syrup Tablets," for a medicinal preparation for human use. A. J. White, Limited, 35, Farringdon Koad, London, E.C., medicine manufacturers. 299,803.
"Jarabe Legitimo Curativo de la Anciana Seigel,' for a> medicinal preparation for human use. A. J. White, Limited, 35, Farringdon Road, London, E.C., medicine manufacturers. 299,800.
"Mother Seigel's Malt Cough Balsam," for a medicinal preparation for human use. A. J. White, Limited, 35, Farringdon Road, London, E.C., medioine manufacturers. 299,804.
Spelling is because of PDF to text conversion.
From here it seams likely it was the same A.J. White.