Can you elaborate on the time the story depicts and the specific laments? Is Sweeny Todd meant to be earlier-mid Victorian (contemporary with, say, Dickens's classics like Oliver Twist and Hard Times), or late Victorian (contemporary with Doyle's Sherlock Holmes stories)? When precisely we're talking about matters a lot for the questions of meat, prices, and especially purity.
Based on our previous exchange, Sweeney Todd came out in 1846; I'll start by admitting that I know nothing of the story save the not-awesome Johnny Depp movie. But, I do know some things about food in Victorian Britain!
So, first off, it's possible that cat and dog meat was actually for sale. Henry Mayhew, in his 1851 London Labour and the London Poor. Mayhew was what we might think of as a "proto-ethnographer." He wanted to report on the wide variety of people inhabiting the metropolis and how they earned their bread (his exact phrase was "pick up a crust"), and to that end he surveyed the many people who sold various sorts of edibles. I've taken a photograph of p. 5 of my edition of the book so you can see the variety, and note that it includes a range of foods that we would probably not want to eat today, along with some familiar items. In the former category are asses' milk and the aforementioned cat and dog's meat, while the latter category includes things like peas, baked potatoes, lemonade, and cough drops. Sheeps' trotters might be somewhere in between, as I've seen them offered in a restaurant, but they didn't seem to be very popular. Mayhew also, of course, notes that there were pie sellers as well.
Now, the cat and dog's meat that Mayhew mentions here is the only time I've seen it, and Mayhew was very much a middle class person, writing for a middle class audience, and the whole tone of his writing suggests a person writing about foreigners. That's right in line with what we know of class relations in early and mid-Victorian class relations: to the middle and upper classes, the working class were Others, truly different kinds of people, semi-savages who needed the firm disciplinary guidance of the betters. This guidance took many forms, from the Poor Law that obligated all to labor for whatever wages they could obtain or resort to the Workhouse where they could expect the most meager meals in exchange for hard labor and constant humiliation, to religious moralizing, to outright incarceration. Bearing that in mind, it's entirely possible that Mayhew was simply repeating the most lurid tales of barbaric, poverty-stricken inhabitants of London; as I said, I've never seen another mention of it, and I've surveyed an awful lot of working-class diets right through the 19th century. Working class people describe eating the very lowest qualities of meat, bread, and oatmeal, of digging potatoes, turnips, and carrots out of fields, of starving even--but I've never seen another mention of cat or dog meat.
But, class, prejudice aside, why would Mayhew write this, and even more, why would Sweeney Todd include it? Well, the food situation in Britain in the middle of the 19th century was grim. As I outlined in a series of posts last year, the first half of the 19th century was a moment when industrialization had profoundly disrupted and reordered British society, but it was not until at least 1850, and perhaps even later, that the benefits of industrialization actually began to spread to the bulk of society. Indeed, the 1840s were retrospectively dubbed the "Hungry Forties," and while that moniker was bestowed for political reasons as this book from 1904 illustrates, this was a moment when real wages were fairly low, and the various "costs" of living in British cities relatively high. Those costs were not merely rent and prices, but an urban environment that was toxic in many ways. Local and national government had not yet begun to regard the health of the population as an object for state intervention, and thus the market was the only means through which peoples' physical needs were met. As a result, there were repeated epidemics of cholera thanks to poor water supplies (the companies that supplied the water swore up and down that their water was perfectly fine); see Christopher Hamlin's Public Health and Social Justice in the Age of Chadwick (1998), a classic book that really set the standard for scholarship on this topic. Absent municipal sewer and trash services, filth and industrial refuse built up to horrifying levels in the towns and cities, as Friedrich Engels described in his 1848 The Condition of the Working Classes of England. And, most relevant to our discussion, food was almost universally adulterated.
I've discussed food adulteration at this point before, so I'll quote that previous post at length.
Collins ("Food Adulteration and Food Safety in Britain..." 1993) calls the period from 1815 to 1860 the “golden age” for adulteration; P. Mathias, in his classic Retailing Revolution (1967?), attributed the mid-nineteenth century deterioration of food quality to “low money wages translated against high costs in the distributive system and a failure of the distributive trades to advance as fast as urban populations.” In other words, poor but rapidly growing urban populations, and a fragmented and unregulated trade with very slim profit margins combined to produce a situation in which food retailers tried to make a profit any way they could. There was very little to stop them, and in the mid-nineteenth century, food was dreadful indeed. It was at this point that Britain was rapidly transitioning from a majority rural and agrarian society to an urban and industrial one.
[...]
By the early and mid-nineteenth century, people were moving into cities and had no direct access to local food supplies, nor the room or equipment in their smaller, poorer urban dwellings to process their own foods. As such, the food supply of the country became increasingly commercialized. The commercialization of grain had occurred over the eighteenth century as transportation networks improved, and it spread to the rest of Britain's diet in the nineteenth century. The old medieval regulations on food trades were removed, with the last really important one being the Assize of Bread, repealed in London in 1815 and in the Kingdom in 1836. New food retailers and manufacturers went into business to supply the rapidly growing cities, but, as Matthias argued decades ago, this happened extremely quickly, it served very poor consumers, and there was virtually no regulation or oversight. Without guaranteed profits and guild regulation, the food trades entered into vicious competition, and retailers and processors used all kinds of adulterants to lower prices or make an article appear better quality than it actually was. Some adulterants were merely fraudulent, such as watered down milk or margarine mixed with butter, while others were outright harmful, such as arsenic and lead in candy. Tea was notorious for adulterants, which included dirt, sawdust, lead, various industrial chemicals like prussian blue.
Meat in particular was sometimes rubbed with copper to give it a redder appearance, thus making it appear fresher. But, really, the fact that food was almost universally adulterated really came to the fore following The Lancet's 1851 series of investigations of food. Doctors and other medical professionals tested a wide variety of articles of food from London, and then later from the other major cities, and found literally everything adulterated in some way. This ultimately led to legislation beginning in 1860, as discussed in the texts cited above. But, it was not the first time that adulteration scares had gotten significant public attention. In the 1820s, Frederick Accum published several books on the state of food in London, and these were quite alarmist in tone, asserting that adulteration was universal and as bad as one could possibly imagine. And, given the findings of The Lancet a few decades later, perhaps he wasn't so far off.
There's one final aspect to this that merits discussion, and that's the idea of cannibalism. Now, there is no doubt an extensive historiography of the particular horror that Britons felt at cannibalism, particularly as it was the sort of thing that would be attributed to the "savages" they encountered in the far reaches of the empire. I am, however, largely ignorant of that particular historiography. But, there was a relevant and well-publicized scandal in the 1840s at the Andover Union Workhouse. Workhouses were effectively prisons for poor people. If you couldn't feed yourself, you could enter the workhouse, but doing so subjected you to very low diets and lots of menial labor, leavened with systematic humiliation and "discipline." You were not, for example, allowed to leave when you wanted; you could stay for as many days as you wished, but staying for a day effectively put you at their mercy and the officials running the workhouse wouldn't let you leave until the following day. At the Andover Union Workhouse in 1845 and 1846, there were some unusually severe administrators, who also happened to be corrupt, and they made money by reducing diets to very low levels--so low, in fact, that people starved, and reports emerged that prisoners gnawed on the flesh from rotting bones, and perhaps even from cadavers, as outlined in the 1846 House of Commons Select Committee on Andover Union Workhouse. This revelation quite naturally shocked polite society, but I think it combines well with the acknowledgement of cat and dog's meat from Mayhew, the widely known issues of adulteration, and the generally awful conditions of food in British cities at midcentury to point toward the fact that there was some precedent, at least in the public imagination, for a pie shop in the worst parts of London that might serve people-pies.