Daniel Little has a post on Hume as historian at "Understanding Society." I think gets some things right, although I think it also overlooks some very important things.
(1) It is quite true that Hume's History is highly biographical and focused on linear narrative. But I think it's inaccurate to say that "The narrative proceeds from court to parliament to war to plots to trials and executions, with virtually no commentary on the sequence." In fact, none of Hume's contemporaries read him this way: they read it as a continual commentary. In the charged politics of the time it was impossible for them not to do so. Many of the interpretations of events Hume makes were very controversial interpretations; as Hume somewhat melodramatically put it, everyone was united in rage against the man who presumed to shed a tear for King Charles and the Earl of Stafford. (It's also very hyperbolic since the History was very popular, indeed, Hume's most popular work in his lifetime and for a considerable time afterward.) His work was also widely seen as a sustained attack against Calvinism. The reasons for this are important, and lead us to the second point.
(2) We know from Hume's letters that the reason he shortchanges most of England's early history is that it is with the Stuarts that he first could clearly see the operation of factions. And this is exactly what the History of England is: it is a sustained study of factions in the concrete case of England. It is a biographical history, but saying that it is a biographical history makes it sound as if it were just a story of Great Men. But there is a reason it is biographical, and the reason is that factions lift up elites. Factions form around people, or certain people become representative of them, and so forth. All the economic and social context that Little finds missing in Hume is missing because factions don't take them into account except in very limited ways; the oppositions between Court and Country, for instance, were never about finer details of economics or government.
(3) Further, I think it's important to pay close attention to the mechanisms to which Hume explicitly appeals. These mechanisms aren't explained at great length in the History itself; in order to find theoretical discussion of them we have to go to Hume's essays. But they are there. Superstition (or priestcraft) and enthusiasm are posited as playing a real causal role in large parts of the History, for instance. As I've noted before, there's some room to doubt about whether Hume's use of them is sufficiently coherent for them to do the work he clearly thinks they need to be doing, and Hume's Calvinist critics, like MacQueen, pressed his use of superstition and enthusiasm as causal explanations very hard. But the important thing for our purposes is that there is in fact a large scale theoretical explanation of events going on throughout the History, one involving Hume's theories of political and religious factions. That he is less abstract in his explanations than Gibbon is certainly true; but that's because abstractions don't explain: particular events do. Hume's treatment of the particular events as explanatory, however, does involve a real theoretical set of ideas about how explanation in historical matters should work. It's just not right to say that there are no explanatory themes in the work; every page is full of them, and what is more, they were recognized as such, and criticized as such, by Hume's contemporaries.