I read that Cromwell tried a lot of different governmental things during his rule in England, but I can't quite recall where I read that he abolished private property specifically, and my google-fu is turning up nothing. Did that actually happen, or am I under Mandela's spell?
Not my usual field, but I think you ( or someone) may be confusing the government of England during the Interregnum, and under Cromwell, with one or more of the diverse (very diverse) religious groups that appeared during the chaotic period of the English Civil War, after the king had been defeated and executed and parliamentary authority was somewhat vague.
With the removal of the king, some began to question the whole need for hierarchy, both in civil and religious affairs ( though at this time there was not a very strong division between civil and religious). Those demanding civil equality were called Levellers, questioning the the need for kings, lords, dukes, etc.. Similarly, one strain of religious thought was that , ultimately, God resided within people , as opposed to being some kind of authority held by a hierarchical church. Three groups who embraced this idea were the Quakers, (who continue to this day), Ranters ( whom you could call Extreme Quakers, who would say that, beyond God being within them, they WERE God) and a group called the Diggers. These appeared in Surrey in 1649, went to a large piece of common land near Cobham ( a place where the village would tend to graze livestock) and began to plant vegetables, saying they would also feed and clothe any in need. Eventually they were moved off, but other colonies of them appeared. Like many of these groups, they did not last beyond the 1650's. And like many of these groups, they had access to a printing press ( the English Civil War was a great time, if you were a printer) and a spokesman, in their case, Gerrard Winstanley.
Their story has been pretty durable. I think some Marxists have tried to claim them, and their communal lifestyle was embraced by some of the hippies in the 60's in San Francisco , who also called themselves Diggers and handed out free good and clothing, mostly it seems to other hippies ( but this is waaay outside my field)
In any case, Cromwell was decidedly NOT in one of these groups, was never a Leveller. But the New Model Army, sometimes the ultimate power in the country, did have Levellers in it. His efforts to negotiate with them and try to keep them from seizing control may be seen in the famous Putney Debates
The Quakers have also tended to keep some of Winstanley's writings in print, but some is now online, like his True Levellers Standard Advanced