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SHORT ANSWER
Probably the most widely expressed view on American Independence from Britain was that it was inevitable. Whig historians, in particular, also say the revolution was justifiable and that the colonists' cause was a just one. Some writers also express regret, particularly that the separation did not happen peacefully.
On the Founding Fathers, criticism is hard to find; they were generally held in high regard. However, one exception is perhaps Thomas Jefferson.
On the Declaration of Independence and the ideals expressed therein, there is little criticism except the *hypocrisy concerning slavery. By the late nineteenth century, July 4th celebrations in England were held in some municipalities and even the Royal Navy took part on one occasion.
There are also a number of other 'interesting' views expressed by individuals, such as the famous Macaulay quote that the constitution was "all sail and no anchor" (see below for context) while one politician felt that the only things America lacked were a King and a House of Lords.
GENERAL POINTS
Given the length of the Victorian era and the diversity of the personalities who put pen to paper on the subject of the American Revolution, a fairly wide range of observations can be found, reflecting the often different perspectives and interests of their writers. However, if one had to identify one dominant ‘thought’ it would be that the separation of the colonies from the mother country was, ultimately, inevitable.
The non-historians among these writers mostly commented on contemporary (for them) America and Americans but at times reveal their thoughts on earlier events. That said, what follows is unfortunately mostly limited to writers as there seems to be little on record as to what the rest of the population (i.e. the vast majority) thought. We can, though, surmise that at least some would have been influenced by what the writers published.
Among historians, much of what was written on the American Revolution for most of the Victorian period was penned (unsurprisingly) by American historians, foremost amongst them George Bancroft whose
liberal patriotism was generally shared by historians outside of the U.S., including W.E.H. Lecky and George Otto Trevelyan, and was hugely influential in his day
Source: The American Revolution: a historiographical introduction
For these Whig historians
...the underlying and unifying theme of American history was a Providential march toward liberty and democracy away from the tyranny and absolutism of the Old World.
British imperialist writers from the latter part of the Victorian age accepted that the American colonies had been badly treated and that the revolution was justified. Nonetheless, as Laurence Kitzan in Victorian Writers and the Image of Empire explains,
...it was a matter of regret that the wealthiest...region with the greatest potential had...broken away from the empire before the imperialist writers began to write. The American Revolution and the demise of the American colonies as part of the imperial system was always an embarrassment to the writers.
After the American Civil War, there was "intensified Anglo-American” interaction . One interesting example of this is cited by Brook Miller in America and the British Imaginary in Turn-of-the-Twentieth-Century Literature, giving us a glimpse of how some people (other than writers) viewed the American Revolution:
at the close of the nineteenth century.... municipal governments held American Independence Day celebrations in London and many of Britain’s smaller cities.
Even the Royal Navy got in on the act in 1899 when
in Plymouth, England, all the British warships there are decorated with flags and a 21-gun salute is fired
SOME VIEWS OF INDIVIDUALS (in roughly chronological order)
Frances Trollope (novelist) wrote Domestic Manners of the Americans (1832) just before the Victorian era (and thus not long after Britain and America had been at war) but it is worth citing for the controversy it caused and because her views contrasted sharply with those of her son, Anthony Trollope (see below). Also, she lived 25 years into the Victorian era and I've found no evidence that her views changed.
For Frances Trollope, the history of British-American relations is a history of rupture, with the American Revolution (1775-83) creating an absolute break between the two nations. In her account, the Americans rejected everything they had inherited from the British, while creating almost nothing to put in its place.
Source: Amanda Claybaugh, Trollope in America (in The Cambridge Companion to Anthony Trollope)
Early in the reign of Queen Victoria, Charles Dickens visited America and published shortly thereafter his American Notes (1842). His comments are almost entirely about contemporary America but, in the course of decrying the American press, he reveals his admiration for the founding fathers:
...while the newspaper press of America is in, or near, its present abject state, high moral improvement in that country is hopeless. Year by year, it must and will go back; year by year, the tone of public feeling must sink lower down; year by year, the Congress and the Senate must become of less account before all decent men; and year by year, the memory of the Great Fathers of the Revolution must be outraged more and more, in the bad life of their degenerate child.
Harriet Martineau (social theorist and Whig writer) admired the republican ideals of America,
particularly the ideal of equality as enunciated in the Declaration of Independence, and was saddened to see in America a chasm between theory and reality... Martineau was the most critical of the Americans in the areas where she believed they glaringly flouted their own vaunted ideals—most notably in the treatment of women and blacks.
Source: Robert Frankel, Observing America
Sir Archibald Allison (advocate and historian) wrote an article titled Foreign Affairs which appeared in Blackwood's Edinburgh magazine. v.57 1845. Blackwood’s was a Tory monthly magazine which published essays and fiction, with contributors such as Joseph Conrad, George Eliot and Samuel Taylor Cooleridge. It had a loyal readership, especially in the colonial service. Allison wrote:
When, in the year 1776, the British colonies, now known as the United States of America, made their declaration of independence, the struggle that ensued was unmarked by any circumstances of particular atrocity or blood-thirstiness, except perhaps, occasionally, on the part of the Indian allies of either party. The fight was between men of the same race, who had been accustomed to look upon each other as countrymen and brothers, and whose sympathies and feelings were in many respects in unison; it was fought manfully and fairly...
Comparing the American revolution most favourably with that of its southern neighbour Mexico, Allison added that
the young and vigorous country which, having attained its majority, and feeling itself able to dispense with parental guardianship, asserted its independence, and vindicated it, with a strong hand, it is true, but yet with a warm heart and a cool judgment.
Despite the generally positive view of British Whig historians, there were major reservations also. Thomas Babington Macaulay (historian and politician) expressed some of these in a letter dated May 23 1857 to Henry S. Randall, an American writer and politician. In the letter, Macaulay – who had “not a high opinion of Mr. Jefferson” expresses his belief that
... institutions purely democratic must, sooner or later, destroy liberty, or civilisation, or both.... Your fate I believe to be certain... the time will come when New England will be as thickly peopled as old England. Wages will be as low, and will fluctuate as much with you as with us. You will have your Manchesters and Birminghams; and, in those Manchesters and Birminghams, hundreds of thousands of artisans will assuredly be sometimes out of work. Then your institutions will be fairly brought to the test.... It is quite plain that your government will never be able to restrain a distressed and discontented majority.....There will be, I fear, spoliation. The spoliation will increase the distress. The distress will produce fresh spoliation. There is nothing to stop you. Your constitution is all sail and no anchor. As I said before, when a society has entered on this downward progress, either civilisation or liberty must perish.
Anthony Trollope (novelist) was far more positive about the American Revolution than his mother Frances (see above). Amanda Claybaugh observes that he viewed
...the American Revolution as a painful but necessary stage in the history of British colonialism. Once the British established a settler colony in North America, it was inevitable, in his account, that the colonists would one day rise up against them, inevitable that the British would try to put them down, and inevitable that the Americans would ultimately succeed in winning their independence. Viewing the American Revolution in this way, Trollope does not see it as a rupture.
John Robert Seeley (historian and political essayist), in The Expansion of England (1883), saw the revolution as being of great importance as it led to a new state bigger in territory and population than any European country except Russia. Thus,
...the American revolution, instead of being a tiresome unfortunate business which may be dispatched in a very brief narrative, is an event not only of greater importance but on an altogether higher level of importance than almost any other in modern English history
Self-described anti-imperialist historian Goldwin Smith was one of a number of writers in the late 19th century who focused on the importance of the Anglo-Saxon link between Britain and America. In The Schism in the Anglo-Saxon Race (1887), which he delivered to the Canadian Club of New York, he bemoans what he sees as the Anglo-Saxon tendency to quarrel easily, adding
While the cannon of the Fourth of July are being fired, and the speeches are being made in honor of American Independence, we, though we rejoice in the birth of the American Republic, must toll the bell of mourning for the schism in the Anglo-Saxon race....
The relation of political dependence between an Anglo-Saxon colony and its mother country was probably from the beginning unsound, and being unsound it was always fraught with the danger of a violent rupture.
He is sharply critical of the way the British handled the colonies
There seems reason to believe that fully one-half of the people including a fair share of intelligence, remained at least passively loyal till the blundering arrogance and violence of the royal officers estranged multitudes from the royal cause.
He also had a low opinion of Jefferson:
Jefferson was a Rousseauist and a French revolutionist in advance.... A true brother of Rousseau who preached domestic reform and sent his own children to the foundling hospital, Jefferson declaimed against slavery and kept his slaves. His theories may have been true and his sentiments may have been beautiful, but the British Government could not have been reasonably expected to shape its colonial policy so as to satisfy a Rousseauist and a Jacobin.
Like almost all other writers, he felt that
At all events separation was inevitable; it was impossible that the Anglo-Saxon realm in both hemispheres should remain forever under one government,... What is to be deplored, if any foresight or statesmanship could have prevented it, is the violent rupture.
The poet and cultural critic Matthew Arnold felt that only Washington and Hamilton were men of “distinction” (in Robert Frankel, Observing America) but nonetheless saw fit to cite Edmund Burke's “impressive and profound words” in his Civilization in the United States (1888):
A great revolution has happened — a revolution made, not by chopping and changing of power in any of the existing states, but by the appearance of a new state, of a new species, in a new part of the globe. It has made as great a change in all the relations, and balances, and gravitations of power, as the appearance of a new planet would in the system of the solar world.
Arnold also mentions soldier and politician Hussey Vivian as being “delighted” with America but that they should have a king and replace the senate with a House of Lords.
Newspaper editor W. T. Stead was a noted promoter of Anglo-American unity, going so far as to make
the case for the observance of the Fourth of July throughout the English-speaking world by contending that the American Revolution had embodied traditional British political principles and that the cataclysm had taught the crown a valuable lesson about how to sustain a viable world empire.
Source: Robert Frankel
Stead, like Martineau, was also highly critical of slavery, saying it made the Declaration of Indepedence sound 'hollow' in the slave states.