I'd strongly recommend Robin Fleming's Britain After Rome (2010) for a look at local community life, mostly based in archaeology. Guy Halsall's Worlds of Arthur (2013) for the political situation, dismissing the one highly unreliable source we have (Gildas) and instead using archaeological comparisons with France to draw on the more reliable textual sources we have there (Gregory of Tours, etc.).

And as for farming, there's no thorough survey that I know of for England, but look to Fergus Kelly's Early Irish Farming, which reaches back as far as Insular sources let us, i.e. into the early 600s (although the manuscripts are no older than the 1100s, which is a bit of a concern). It's encyclopedic and will answer any questions you might have, although because it's about Ireland the particulars won't be quite right and the emphasis may be a bit off. For example, much of England would be less pastoral and more agrarian than Kelly's Ireland (fewer cows, more wheat aka corn in the Queen's English). But if you read Fleming and look to Kelly as a reference for describing the types of rural life that she mentions, you'll end up with a pretty good picture of what things were really like.

There was a pretty big shift in rural life during the period you describe (400-600), from the heavy and labor-intensive farming of Romano-British villas to the less productive but easier to cultivate uplands in many places. This change in location was at one time thought to be evidence of large-scale Anglo-Saxon colonization, although most scholars now see this period as only a slight uptick in immigration from abroad accompanied by a major cultural revolution at home.

There were good reasons to move to the looser but less productive soils uphill: you didn't have to work as hard because you were no longer worried about paying Roman taxes (or being a Roman slave), but without the Roman economy, you also needed to find time to make many things at home (pottery, leather, textiles) that your ancestors could have bought in a Roman market or received as 'gifts' from the elite patrons who received much of their harvest in turn.

But overall, I would downplay the 'Saxon' v 'Celtic' differences you suggest. We have no record that people in the 400s-600s would have thought of themselves in these ways, or that these words would have even made sense to them (although that changes in the early 700s). Scholars working in the 1800s, who were obsessed with languages and mythologies (which were cornerstones of national identities in the early days of nation-states), started using them as a primary category for describing the peoples of the early middle ages. And scholars today continue using the terms out of convenience, although generally acknowledging that these words mean more about how we organize our studies of the past than they do about how people in the past actually organized their lives.

There were major differences between Ireland and England, but there were major differences within these regions as well, resulting from both geographic (e.g. where is it good to raise cattle?) and cultural (e.g. where do people prefer living in urban environments where livestock are poorly suited to serve as measures of wealth?) factors. So yes, please do look for differences, but I'd encourage you to think of them in terms of micro-communities rather than big cultural groups. If you take a close read of Fleming's Britain After Rome, you'll see why. Happy reading!