What if the Levellers came out over Cromwell's Grandees

I'm working on a little project, which mostly pins on this idea, if the Leveller faction of the Parliamentarians in the Civil War, how would this change the course of both British history and global history.

I'm mostly looking into the initial rule of the Levellers, their relations with other nations and if certain conflicts, like the Anglo-Scottish War, conquest of Ireland, Seven Years War would still occur as they did in our time.