Forms of land-ownership were diverse, both across the Celtic-speaking world in general and within Britain. Some general principles which might be valid for one area might be totally different in another, varying with agricultural practice or cultural norms.

That said, if you declared that a certain patch of land was 'your plot', at least people would know what you were talking about. Starting from the late Bronze Age (agricultural practices don't neatly follow the three-ages system), and up to the Roman period, basically all of England was covered with coaxial field systems. Probably not all plots were in use at the same time, but the extended use of many of these plots (with continual investment to ensure soil quality, including manuring and acidity regulation) hints that these were enduring structures, perhaps even more so than the continental variety where field-shifting was practiced instead.

The history coaxial field systems is still an ongoing subject of research, because until recently they were extremely hard to date. The pre-Roman Iron Age has a tricky calibration curve for radiocarbon, which means the method is useless in distinguishing between 800 and 400 BC, and ceramic styles are not particularly time-sensitive either in this period. Still, we know there are changes in agricultural practice just before the Roman conquest, which corresponds to changes in Iron Age society as a whole (the re-occupation and increase of activity on the hill-forts, or the increase in warfare and human sacrifice for example). This also leads to an increase in the area of arable land, by burning forests and draining marsh, but also a more intensive use of the land already plotted out. Roman villa-based commercial agriculture of course upset this native system entirely, but it should not be underestimated to what extent they simply built upon existing practices.

The idea of 'communal lands' is really more of a medieval thing. While non-owned out-fields (upland for grazing, moorland for peat, forests for wood or hunting) existed before, their ownership/access rights are more contested in the pre-roman period than 'tribally owned'. This is what made cattle raiding feasible.