This is an interesting question and something that people have been wondering about for a long time. Before I can answer it, I feel like it is worth disclaiming that I am not British, in terms of national origin. I am American, was educated from elementary school through my graduate program entirely in America, so when I speak here, I am talking about what academic historians say about the American Revolution on the university level stage. I have no knowledge what schools, books, or teachers say for students beneath college level. Fortunately, since the American Revolution is something studied globally, I’ve studied historiographical debates of modern and previous historians in Britain, and I will be happy to discuss that here.

Overall, the majority of historians who studied and reported on the American Revolution currently have no major conflicts with American historians who study the same time period, but this is not true for all of the last two centuries. The first person to tackle this question was British historian Richard Middleton, who conducted research and wrote about it in his article, “British Historians and the American Revolution” . His article mainly seeks to study what early British historians said and reported on the American Revolution. I feel obligated to point out that in these early days of the discipline of academic history scholarship, being objective was not something that was desired.

Early historians, generally speaking had very little problem with letting their biases show. This drastically changed during the middle of the 20th century, as historians sought to become more objective in their study and reporting of history. It’s also worth noting that the vast majority of British scholarship in the first century and a half after the American Revolution took place was mainly focused on British perspectives; such as British politics and economics during that period. Americans, especially during the 19th century conducted a lot of history related to the biographies of the "Founding Fathers" and also many sub-topics within the war itself (like military history of the Continental Army). Far fewer British historians studied American perspectives on the war, such as the Continental Congress, the Founding Fathers, or the Contiental Army.

Middleton noted that many British historians were British apologists, who did side more favorably with the British Crown's decisions during the war and were very critical of the rebelling colonists. This article does a few interesting things, first it accounts for a history of early British Historians who studied the American Revolution and notes that some of the early historians from the late 18th century were in fact more favorable in their views of the rebelling colonists, but they were the minority. Historians tended to be torn between two radical positions in the U.K. One historian, Sir George Otto Trevelyan created a three-volumne account of the American Revolutionary War between 1874 and 1880. Trevelyan, a liberal, reported that the first twenty years of King George III’s reign was a period of regression for English laws and and rights. His writing reflects that the Americans were justified in overthrowing the British government, calling the Americans “law respecting people, who did not care to encroach on the privileges of others and liked still less to have their own rights invaded.’ [Middleton, 50]. This created one of the first historiographical debates in this particular field, with other men, like William Massey and William Lecky arguing for the traditional “Tory” view of the war. Where Trevelyan came down hard on royal governors and British officials in America, historians like Lecky was much more gentle on them, saying that they were just loyal men trying to fulfil their duties to the King. [Middleton 51]. Ultimtely, Middleton noted a few key differences between these earlier types of scholarship between American and British scholarship on the war:

From this study of British historians and the American Revolution, one or ore general conclusions can be drawn. In the first place, there has bee na curious dichotomy between scholars on both sides of the Atlantic as to what actually constituted the Revolution. Most British writers do not appear to consider it to be properly underway until the fateful year of 1775, while for most American writers, it was then merely a matter of dotting the ‘i’s’ and crossing the ‘t’s’ on the declaration of independence [sic]. There has also been little attempt to understand the revolt of the thirteen colonies by analysis of their social, economic, or politiocal development, lines of approach for so long popular with the American historians. [Middleton, 58]

Historians during the 20th century, especially in the post World War II era appeared to settle more soundly into the more objective approach to history. Middleton spoke also of, at the time of the publication of that article in 1971, how there was a revival of the British study of the American Revolution during his present because of the infusion of American culture, history, and politics that exploded in those preceding decades. [Middleton, 56] In recent history, the vast majority of historical scholarship that has come out (at least as what I’ve seen and studied] has not conflicted with the current consensus of scholarship coming out of the United States. Some British historians, like Stanley Weintraub’s Iron Tears has pointed out some differences that he sees in views of the American Revolution, but nothing really seems too far out that it would conflict with what other historians would say. For instance, he shows that from the British perspective, the “taxation without representation” rallying cry of the colonists was a bit weak of an argument from the British perspective because many of the Englishmen living in England were not represented in Parliament either. (His book though more-so focuses on how the Average person in Britain felt about the war, rather than focusing on Historians studying that period).

Overall, modern scholarship between historians of the United States and Britain tends to add to the historical conversation in general on this topic, rather than causing conflict between them. Historians will disagree in every field, it's why consensus does not have the same power as a fact, but there isn't anything fundamentally different between scholarship coming out of the U.K. versus what is coming out of the United States or other countries.

Edit: fixed typos

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Quick preface: I see uncovered-history wrote a response while I was typing up mine. I think they complement each other nicely.

While there are certainly still major disagreements about the American Revolution, I cannot think of any that break down primarily along those geographic/national lines. The context in which we live and our backgrounds do shape the kinds of questions we ask about history, though especially in our globalized world today, I don't see any areas in which we are talking past one another.

I do think the differences in our approaches used to be more distinctive. In the mid-twentieth century, the major schools explaining the origins of the American Revolution were generally aligned with one's political sentiments. A conservative approach emerged after WWII aligning with Cold War-era thinking. Historians (for example, Richard Hofstader) argued that the Revolution was fundamentally not as a radical overthrow of the social order but instead an attempt by Americans to preserve their rights and liberties. They emphasize the democratic, literate, informed nature of Revolutionary-era Americans.

Historians in the neo-whig school disagreed and argued that the American Revolution was fundamentally a political and social upheaval generated by political ideas. The paradigmatic work in this vein would be Bernard Bailyn's The Ideological Origins of the American Revolution. Other historians in this vein include Pauline Maier (a Bailyn student) and Gordon Wood (though I personally think Wood is a bit more liberal and writes a bit more toward consensus than the other historians in this school).

The neo-Whig approach, which focused on the political and intellectual worlds of middling and upper-class people, was challenged as the academy itself expanded and diversified in the 1970s. Historians on the left have emphasized the role of ordinary people and devoted more attention to aspects of race, class, and gender. These historians focus on economic and social explanations for the Revolution and often regard ideological or political rhetoric of the period as hollow. Instead of seeing the Revolution as a contest for independence (home rule), they see it as a question of power on the ground in America (who would rule at home). Historians in this vein include people like Jesse Lemisch, Gary Nash, Woody Holton, and Tim Breen.

While Britain had some parallel experiences in the twentieth century, the above examples are of American scholars writing in the context of American debates and issues. (By contrast, during the mid-twentieth century, British attention on the period surrounding the American Revolution was centered around the work of Lewis Namier, a Polish-Jewish emigrant to Britain. His approach was heavily influenced by the context of the world wars, and in particular, he saw the British state as one that would never fall to absolutism. He focused on the personal biographies of individual politicians, showing how alliances shifted and how the party system was based on personal animosities, loyalties, and local issues, rather than any larger ideological positioning.)

Constitutional explanations for the Revolution seem to have maintained more popularity among historians in the U.K. I don't think it's unfair for us to say that British scholars probably inherently care more about the British constitution and probably understood it better, especially in the days when early Americanists were trained solely in colonial American history. The constitutional approach was in fact an old way of explaining the conflict. (The work of Charles McIlwain in the 1920s is probably the best-known example). However, Harry Dickinson, an English historian working in Edinburgh, has been explaining the constitutional origins of the crisis since the 1970s. More recently though, prominent U.S. historians (including Jack Greene, Patrick Griffin, and Brendan McConville) have picked up on this line of thought.

One of the current trends in scholarship about the American Revolution is placing the conflict within the imperial context. Scholars on/from both sides of the Atlantic are doing this work (e.g. Stephen Conway, Andrew O'Shaughnessy, Eric Nelson, Justin Du Rivage). Advances in technology, I would argue, both in ease of travel to archives and digitization of records, have made this approach more doable in recent years.

I would argue, perhaps, that perhaps one way the American and British views of the war had differed was in valuing the competence of British military strategy during the conflict. The book The Men who Lost America by Andrew O'Shaughnessy (a British-born scholar who's now based in the U.S.) demonstrated that we have drastically underestimated the skill of British politicians and officers in addressing the complexities of the war. I mention it as an example of how our backgrounds do influence what we see and how we approach this very well-trodden historical ground. For instance, scholarship on the place of Native people in the Revolution has been led almost entirely by scholars from the U.S. (e.g. Peter Silver, Greg Dowd), though historians working on the American Revolution in the U.K. would not deny the importance of that work. Ultimately, we are all reading one another's work, as well working, traveling, and conversing across the Atlantic.

(Edit for a few typos.)

As a Brit living in America, I keep getting asked about the revolution as if everyone in England sits at home and cries about it when in reality we don’t actually care and it was a time little speck on British history