Bagehot's 1873 book, Lombard Street: A Description of the Money Market, is an application of Bagehot's theories of sovereignty described in The English Constitution. In this, we can draw an analogy: The English Constitution is to Lombard Street, as Smith's The Theory of Moral Sentiments (1759) is to The Wealth of Nations (1776). Both men applied their philosophical orientation more or less consistently in books that attempt to describe the way economic society works.
There is, however, a significant difference between these two influential thinkers. Where Smith dismissed the idea of widespread ownership of the means of production as essentially irrelevant, falling into an inadvertent elitism, Bagehot embraced a political — and thus economic — system that assumed a political (and thereby financial) elite as a given and a positive good, as a necessity, in fact, if society is to advance socially, economically, and politically. Less than half a century later Keynes would take Bagehot's assertions as proven fact, and base his entire economic theory on the assumption of the absolute necessity for existing accumulations of savings to finance capital formation.
On the other hand, consistent with his "invisible hand" argument, Smith believed that the fundamental human right to own a meaningful amount of capital is adequately secured through our possession of human labor. Since he reasoned that those with property in capital will always require the labor of those without property in capital to satisfy their wants and needs, human labor will always be in demand. The worker who owns no capital will always be able to enjoy an adequate and secure income through the sale of his labor. Legal title to the means of production doesn't matter because (as others came to accept as a matter of course), "Neither capital can do without labor, nor labor without capital." (Leo XIII, Rerum Novarum, § 28.)
A problem surfaces, however, when technology begins to take over the bulk of the manual input to production, replacing human toil. As Charles Babbage pointed out in his essay, On the Economy of Machinery and Manufactures (1835), while technology makes for an independent (though not autonomous) addition to the mere animal power of humanity, it does not change a human being's physical capabilities:
"(4.) The advantages which are derived from machinery and manufactures seem to arise principally from three sources: The addition which they make to human power. — The economy they produce of human time. — The conversion of substances apparently common and worthless into valuable products.
"(5.) Of additions to human power. With respect to the first of these causes, the forces derived from wind, from water, and from steam, present themselves to the mind of every one; these are, in fact, additions to human power, and will be considered in a future page: there are, however, other sources of its increase, by which the animal force of the individual is itself made to act with far greater than its unassisted power; and to these we shall at present confine our observations." (Charles Babbage, On the Economy of Machinery and Manufactures. London: Charles Knight, 1835, 6.)
Because the income generated by technology belongs by natural right to the owner(s) of the technology, the propertyless worker is left out in the cold. A similar problem happens when companies shift factories to areas or countries that have lower wage rates. Jobs disappear, and society is disrupted. Technological advance and globalization, morally neutral yet potentially beneficial things, become perceived as inherently and objectively evil.
What Smith might consider an unfortunate but inevitable working of economic laws (actually a distortion of economic laws), however, Bagehot, and Keynes after him, regarded as the proper ordering of society. Like Keynes, Bagehot rejected the substance of democracy, while calling his system democratic. The only real issue was whether the elite that controlled the economy should be an unaccountable private elite, as Bagehot supposed, or a marginally accountable public elite, as Keynes proposed. This, of course, depended on who controlled money and credit, and thus both political and economic power.