Mimi Matthews in this blog describes how patent medicines were everywhere in he 18th and 19th century:
“These various powders, potions, elixirs, and cordials were primarily peddled by quacks, some of whom purported to be doctors from respected universities. The claims they made on behalf of their products were extraordinary. According to advertisements of the era, a restorative cordial or tonic could do practically anything, from curing dropsy in children to curing impotence in men and hysteria in women. Some even proclaimed that they could cure a fellow of the desire to engage in that “solitary, melancholy practice” s (masturbation).”
I would recommend reading Mimi Matthews blog in full, as what follows here are edited extracts:
An 1805 edition of The London Medical and Physical Journal titled “Of Quacks and Empiricism” set out the facts of Brodum’s life: not only was Dr. William Brodum not a doctor, but he was not even William Brodum. His real name was Issachar Bear Cohen. The article states:
“We announce that he was born in Copenhagen, the capital of Denmark; in the streets of which he early exercised a public profession, that of hawking and selling ribbons, similar to some of his brethren in London, who dispose of shoe-strings in every avenue near the Royal Exchange.”
In 1787, at the age of twenty, Cohen migrated to London where he went into the service of Dr. Lamert – purveyor of Switzer’s Balm.
It was while out hawking Switzer’s Balm that Cohen met a widow who esteemed him very highly. She lived in a town where an apothecary by the name of Brodum had recently died. The widow encouraged Cohen to take the name of Brodum. She also gave him a smart set of clothes. Not long after, the man now known as William Brodum was admitted as a partner in Lamert’s business where he began to represent himself as a surgeon who had served in America with the Hessian army. But Brodum was not satisfied with being a mere surgeon. He had an eye toward becoming a physician. As luck would have it, at that time in history, at certain Universities:
“…the professors have been in the practice of conferring the degree of doctor of medicine, without the least examination, or personal knowledge of the candidate; but merely on the recommendation of some respectable physician.”
After finding such a physician to recommend him, Brodum was appointed a Doctor of Physic by the University of Aberdeen:
[It is understood that this ‘DIPLOMA’ cost William Brodum13 guineas]
What Brodum lacked in medical knowledge, he made up for in “the science of knowing the weakness of human nature.” Passing himself off as a “learned graduate of the University of Aberdeen” (a place that he had never seen before in his life), Brodum rapidly rose to fame and fortune peddling his Nervous Cordial.
“This medicine was chiefly the old formula of the decoction of the woods, consisting of sassafras, guaiacum, and a few other articles, which [Brodum] procured of Mr. Chamberlin, an eminent chemist in Fleet Street. The decoction is well edulcorated with sugar or molasses, and sold at six shillings and sixpence a bottle, or one pound two shilling for five bottles.”
Brodum’s income in 1805 was estimated at five thousand pounds per annum and he was known to own “the most superb carriage in the metropolis,” in which he rode through the streets “in the midst of a gaping and admiring multitude.” He was a convivial man, a true salesman, and was widely liked not only for his Nervous Cordial, but for the generous donations he made to worthy causes – donations for which he made sure he was always credited in the newspaper.
The following comes from a blog written for the Wellcome Library: The Georgian medicine vendor as physician: William Brodum
William Brodum was one of several members of the Georgian medical fringe who were portrayed by caricaturists . . . Brodum is dignified by an entry in the Oxford Dictionary of National Biography , where evidence is cited that he was a Danish Jew, born Issachar Cohen in Copenhagen around 1767. He came to England around 1787 to work for another medicine vendor (Dr Bossy), using the name William Brodum. He obtained an Aberdeen M.D. degree in 1791, and from his house at 9 Albion Street, Blackfriars Road, London, launched his own career as a medicine vendor, specializing in two product lines: “Doctor Brodum’s Botanical Syrup for the cure of scorbutic, leprous and scrofulous complaints” and “Doctor Brodum’s Nervous Cordial for the cure of consumptive, nervous and debilitated constitutions, and people who have been in hot countries”. His advertising for these products included a lot of code words that were euphemisms for syphilis (debility, leprosy, nervous weakness etc.), and the same insinuation was gracefully made in the title and body of a two-volume publication, Guide to old age, or, A cure for the indiscretions of youth (1795), dedicated to King George III, whose favour he received. 
Brodum was therefore both a commercial medicine vendor and a doctor of medicine. Since the two professions were theoretically distinct and incompatible, problems could arise with the regulatory bodies, one of which was the Royal College of Physicians of London. In practice, this combination was not unusual at the time: Sir Hans Sloane, Dr Robert James, and Dr Richard Mead were among physicians associated with proprietary medicines (chocolate in Sloane’s case), a fact which led one commentator to ask “Have not members of the College dined at Dr Brodum’s table?” In any case, Brodum was summoned before the College and told he could not accept consultation fees and should remove from his house the brass plate which described him as “Dr Brodum”. Brodum refused to accept this ruling, and the academic authorities in Aberdeen did not appreciate the College’s scorn for the value of their doctorate. Brodum continued to visit patients for an advertised cost of 5 guineas a week, while outpatients could visit him at his house every Monday, Tuesday or Wednesday.
The following summary comes from: The Patent Medicines Industry in late Georgian England: A
Respectable Alternative to both Regular Medicine and Irregular Practice by Mackintosh:
Contemporary observers frequently bestowed the title of ‘quack’ on the irregular owners. The most notorious was William Brodum (died 1824):
Brodum was regarded as an irregular practitioner, with medicine ownership only as part of his practice.
He was very successful, earning an estimated £5,000 a year from selling medicines. He attracted widespread criticism and satire, with his name repeatedly being used as an exemplar of quackery.