Cromwell's reputation suffered a massive increase during the Victorian Era. For much of English history until that point Cromwell had been just generally disliked across the board; mainly because he'd been a less than stellar ruler and his time in power saw economic issues (debated if they were truly his fault, but none the less) and a rather strict puritan rule cast over England.

Specifically around the tercentenary of Queen Victorian, but just in general throughout the period Cromwell's image was vastly rehabilitated. The movement to rehabilitate Cromwell gained a near cult like status and became known as Victorian Cromwellianism. It got really serious as well, to the point where one Cromwell devotee claimed:

It is a sign of the modern boldness in dealing with the memory of Cromwell, that we are able to claim him fearlessly as a saint.

This wasn't necessarily a new phenomenon; English had always recognized Cromwell's talents. However he was viewed as a usurper who used his talents for bad instead of for the good of the country. The Victorian reversal of Cromwell's image changed that perception. For example English historian Thomas Babington Macaulay, would refer to Cromwell as the "greatest prince to ever rule England."

Of course Cromwell still had his haters, but even they softened. Historian William Godwin's History of the Commonwealt had all the usual anger at Cromwell for his Republican leanings, but it portrayed Cromwell as a tragic hero of sorts, with a fatal flaw dooming an otherwise good ruler.

Another important figure is English historian and write Thomasy Carlyle. He wrote several biographies of famous rulers like Frederick the Great and Cromwell. Carlyle was influential to the development of the Great Man Theory of history; he argued that history had "heroes" one of whom was Oliver Cromwell. Carlyle's work on Cromwell was appealing because he tried to present the man from "inside"; he analysed writings by Cromwell and tried to paint an indepth portrait of Cromwell in a way that hadn't really been attempted before.

There was also a religious aspect. For many Cromwell's staunch puritanism was admirable for those who though morals were loosening or for those who just didn't like Catholics. Specifically a movement called the "Nonconformists" people who didn't agree with the church of England (including puritans). They found a representative and guide in Oliver Cromwell and they played a role in reshaping the public discourse and image of Cromwell

Now this was a somewhat one-sided answer, mainly focusing on radicals. There were plenty of moderates with regard to Cromwell who took the good with the bad and tried to paint an accurate picture of Cromwell. And there were those who still just hated him. When the Government decided to build the statue of Cromwell in 1899 there was mass anger. Not the least because there had not been parliamentary approval. There was mass anger, protests from members of parliament, and writers quickly revived the old image of Cromwell as being a ruthless, power hungry, military dictator in the newspaper to draw up anger over the statue.

Victorian's love from Cromwell died off at the beginning of the 20th century. People just sorta of lost interest in the entire period. Eventually academics would revisit the period again, and the picture of Cromwell in history today is definitely still debated; although in my experience academics have been able to find a nice medium between the "he was the devil incarnate" and "he was Jesus reborn" extremes.

Edit:

My main source for this was a chapter called "Cromwell and the Victorians" found in British Intellectual history 1750-1950