From wiki: "The open-field system appears to have developed to maturity between 850 and 1150 AD in England, although documentation is scarce prior to the Domesday Book of 1086" What was used before this?
Bonus question which I might make its own later: After Rome and before Open Field, how much ancient forest would have been standing? In Ian Mortimer's "Time Traveller's Guide to Medieval England" he states that in the 14th century the level of forest cover would have been about equivalent to what it is today.
Unfortunately, I don't have an answer for you offhand, but I think I can point you toward one. The first place to look might be WW. G. Hoskins's The Making of the English Landscape. It's from the 1950s, so it's not exactly current research, but it's a classic in the field. Plus, his whole point is that the 'modern' English landscape is a product of very long historical development. As such, he should give some time to the systems before the Open Field. Give it a look.