As many smokers might know, this herb will sooth the need to cough. A need that it itself contributes to. Short time effects in a habituated individual are the opposite of its long term effects. Believing in a effect you can experience yourself is not difficult.
When this herb was "discovered" by the Europeans they quickly inquired into all of its properties. Being a sacred plant to the Americans ("Indians") used in many healing rituals, this knowledge traveled back, and was adopted.
Tobacco was a true wonder drug, capable od soothing everything, curing everything. Although the Americans thought of its mode of action in much more spiritual ways, the Europaens were much more mechanistic in their understanding.
Nicolás Mondardes (1519–1588), a well-known author and doctor living in Seville, was the first European physician to unabashedly pro- mote tobacco as a medicine. In 1571, in the second part of his widely read compendium of New World plants, Mondardes highlighted tobacco’s healing properties.
Monardes had published a detailed study of all the plants brought back from the Americas to that date titled Joyfull Newes Out of the Newe Founde Worlde in which he prescribed tobacco for almost every common ailment of the time, including toothache, carbuncles, flesh wounds, chilblains, “evill” breath, headaches, and even “cancers” (Monardes 1925), and so provided all the medical justification needed to suggest that the search for the miracle cure-all was over. Thus, in the early stages of the modern era, tobacco was widely understood to be a “divine sent” medicinal remedy (Pego et al. 1995).
Over time, tobacco’s reputation as a miraculous drug diminished, and by the eighteenth century tobacco use in Europe came to be recognized as primarily recreational. Nonetheless, nicotian therapy continued in Europe well into the nineteenth century. In 1800 European physicians were still using tobacco as an antispasmodic for asthma, an enema for intestinal obstructions, and as a diuretic for dropsy and similar disorders. Some even continued to advocate its use as a prophylactic against infectious diseases such as cholera well into the 1890s.
Smoking anything was an official cure for Asthma and other conditions of the throat and lung. While the main ingredient was tobacco, several other herbs were added to increase the effect. Among them belladonna, datura, and our new wonder drug: cannabis. Examples are numerous. These were sold in pharmacies until the 1970s for West-Germany and a little longer in the East. But since the question seems to be about pure and ordinary tobacco cigarettes…
This 1869 advertisement for Dr. Perrin’s “Fumigator” is promoting the smoking of tobacco as a remedy for catarrh, sore throat, loss of voice, and discharges from the head.
For the most part, by the nineteenth century tobacco appears to have become primarily a folk remedy used in the home rather than one commonly prescribed by classically trained and highly skilled physicians.Goodman05
While most of the established medical science community started to see some potential dangers, like from high doses of isolated nicotine, or just to much soot buildup, on the whole they just started to slowly doubt the benefiical effects from inhalation of the pyrolisation products of this material.
That doesn't mean that folk remedy took completely over and forced scientific medical wisdom onto a back bench. Tobacco found a new ally to promote its virtue (and total harmlessness): advertisers.
In 1927 Philip Morris, one of the smaller cigarette manufacturers of the time, advertised one of its brands, Marlboro, […]. Lucky Strike entered the fray on two fronts: it solicited and printed testimonials from European artistes who informed the reader that they had discovered their favourite cigarette in Lucky Strike, a cigarette that was mild and mellow and because of a special process that treated the tobacco—‘It’s Toasted’— Luckies protected your throat.Goodman93
And the same trend continued well into the 50s, when scientific medicine finally started to convince the public – and its own members – of the detrimental effects and dangers of smoking.
After the cancer link was published in Reader's Digest…
The industry initially responded with denial and buck-passing. “You hear stuff all the time about ‘cigarettes are harmful to you’ this that and the other thing,” Arthur Godfrey reassured his television viewers in September 1952. Not to worry. Chesterfields wouldn’t harm your nose, throat, or “accessory organs.” A responsible consulting organization and a competent medical specialist had vouched for it.Courtwright
Which specialist may have vouched for it? Well, some did.
(Pictures lifted from: “The Doctors’ Choice Is America’s Choice”. The Physician in US Cigarette Advertisements, 1930–1953 (2005))
Not every doctor is always at the forefront of knowledge in scientific medicine or not even just up-to-date, today. Some were bought, some are. In the film's setting of the 1920s, this looks entirely plausible. Old knowledge not yet completely gone, new dangers not widely known or accepted as proven, the continued use as a folk remedy and the onslaught of advertisers play nicely together. It might have been an allusion to a real doctor recommending it, a play on the then common advertisments or a signal that a royal was vulnerable to bad advice, whether from quacky physicians or advertising. Additionally it might be completely plausible that Bertie just lied: "It's medicinal."
Not answeering the more global issues from the question, but what led the king into his habit and addiction: When Cigaretts were Acceptable a physicians perspective in: Under the Knife: A History of Surgery in 28 Remarkable Operations and from a biography George VI
David T. Courtwright: "Forces of Habit, Drugs and the Making of the Modern World", Harvard University Press: Cambridge, London, 2001.
Jordan Goodman: "Tobacco in History. The cultures of dependence", Routledge: London, New York, 1993.
Jordan Goodman: "Tobacco in History and Culture. An Encyclopedia, Vol. 2 Native Americans–Zimbabwe", Thomson Gale, Farmington Hills, 2005.