I'll repost an answer I made a while ago, it incidentally describes some of Cromwell's support base and has a lot of citations.

Cromwell was unambiguously a military dictator and could not have continued to rule except for the army's support. That said, any leader must have a body of supporters and a larger group that at least tolerates them. Because of the Restoration in 1660, many people (an excellent example being the Quaker leader George Fox) who had been supportive of Cromwell when he was active later downplayed their support to win favour in a different political climate. This has sometimes created a historiographical illusion that Cromwell lacked supporters.

There were three basic reasons to support Cromwell in the 1650s: peace, property, and religion. The main cause that turned popular opinion against the Stuarts was Charles I's obstinacy in repeatedly restarting the Civil War when it appeared he had no chance of victory: the common people came to hate him for imposing on them the costs of meaningless war and this leads to the regicide. When Charles II continues fighting through the 1650s, making alliances with the Scots etc, a large portion of England is fed up with continued fighting and supports Cromwell because he is the victor God's Providence chose and they want peace now. During the height of the English Revolution, around the execution of Charles I, there were many groups within the Army (levelers etc.) who challenged property rights and called for redistribution and land reform. Cromwell was a firm opponent of this and so won the support of the propertied classes. Finally, and the linked answer goes into more depth here, many dissenting Protestants strongly approve of Cromwell's religious policy of freedom of conscience for Protestants. These people, like Fox, support Cromwell because he allows their preaching and they are concerned about going back to a "bad old days" of enforced tithes and a state Church (especially because in the 1650s the Presbyterians are angling to establish a religious monopoly.)

So lots of people could come around to Cromwellian government one way or another, and the question of their enthusiasm can be muddled by statements they made after Cromwell was overthrown. From the tumultuous point of view of the early 50s, figures as diverse as county gentry and itinerant preachers could take refuge under Cromwell's dictatorship.