pre-emptive TLDR, if you read the text in bold its basically the argument

Whig history could first be said to have originated during the 19th century in histories of the English Civil War. It was a sort of subset of the historicism paradigm, however many of the Whig ideas persisted well into the structuralist age (from c. 1950-1980/90's). Due to the roots of the Whigs themselves and their ideological background I think it would be best to describe Whig history by looking at their view of the English Civil War.

Historians of a more Whig persuasion would take the view parliament was fighting for greater liberties against the tyranny of Charles, they would draw a metaphorical line of human development, the English Civil War was one step on the road to a utopia, a constant progression of civilization. The past was something to learn from, the present was regarded as a positive development compared to what had come before. History was not so much grey as it was black and white, there were good guys and bad guys, there was a very real idea of a 'learning curve'. (ofc if one is to even still believe in any sort of line, it would be very wobbly rather than the gentle curve of progress the Whigs wrote about)

They would be on the Locke side of the ideological spectrum, freedoms of the individual ect. Yet still based in the Hobbes view of the natural state of man as anarchic. The idea of a constitutional monarchy, an elected parliament, the freedoms of man, all that sort of stuff. (as the Whigs drew closer to Marxists c. 1950-c. 1990's there would however be a few republicans amongst their ranks.)

Their oponnents would have been the more 'Tory' historians who followed Hobbes and would write histories showing Charles I as a tragic hero and showing the lack of strong governance led to anarchy.

Of course today under cultural history, the English Civil War is viewed ostensibly as a religious conflict, the idea of the pursuit of freedoms and rights has largely been thrown out as it seems many would be Roundheads and would be Royalists agreed in the need for reform in all areas but that of the Church. Religious differences is the lowest common demoniator, it seems to undercut everything else.

Under the structuralist paradigm the Whig school persisted, the style of their writings didn't change too much. There was much greater influence from Marx, and the histories of the little people became more prevelant (less John Pym, more underlying forces) when I say little people I do not mean a 'Cheese and Worms' (1976) type study, I mean through the use of statistics gathered from the population (often relating to the economy, Christopher Hill, Marxist, even claimed in 1940 that the ECW was between an emergent middle class and the old upper classes), statistics and the like classical structuralist stuff. However this approach was not fully embraced, unlike their Marxist colleagues the Whigs were perhaps less dogmatic and continued to include famous figures within their histories, and crucially also acknowledged the role of less tangiable factors such as religion instead of drawing all roads to the economy.

It seems however with the relative demise of structural history the Whig school is in decline, its great historians are dying off and they are not being replaced. Historaisn no longer write "the history", instead they write "a history". It has been quite a long time since a real meaty work on the English Civil War has been offered up, probably not since John Morrill (of the new-ish cultural school, not really a 'Whig' historian) in the 1980s (if I remember correctly). Now for example a history would be about a smaller issue which was part of a wider event, such as the role of the prayer book in popular culture in England in the 17th century (a la Judith Maltby). Rather than a wider event made up of many smaller issues.

Here is a few selected quotes from the late great Conrad Russell. They sum up the Whig attitude quite well I think. I really love his description of Charles I, I am paraphrasing a bit but I think in a way it sums up the Whig position quite well."Charles I was incompetant, but not so incompetant that he could not cause the country to enter a Civil War", he also says something along the lines of Charles I had an extrodinary ability to "rub people up the wrong way." An obvious sceptism for monarchy, certainly a departure from the pro-Charles works of the 'Tory' school. (or Charles the martyr as some of them might call him)