Partly yes, and partly no. The main narrative sources for English history in this period are monastic chronicles, and many of these chronicles paint a pretty grim picture of the aftermath of the plague. Thomas Walsingham, who compiled his account in the 1390s, described the devastation left in the wake of one outbreak in 1349:

Its destruction was so great that scarcely half mankind was left alive. Towns once packed with people were emptied of their inhabitants, and the plague spread so thickly that the living were hardly able to bury the dead . . . rents dwindled and land was left untilled for want of tenants . . . so much wretchedness followed these ills that afterwards the world could never return to its former state.

Others echoed these apocalyptic overtones:

There was such a shortage of people that there were hardly enough living to look after the sick and bury the dead; so great a multitude was not swept away, it was believed, even by the flood that happened in the days of Noah’.

Some chronicles speak of only one in four people being left alive, while the idea that there were too many corpses to bury is a very common refrain. It’s important to distinguish, however, between reality and rhetoric. It is undoubtedly true that many, many people died, with most recent estimates putting the figure in England at around 40% of the population. While this obviously had profound economic and social consequences, it’s not really appropriate to talk of society collapsing. Medieval society was far more resilient than we are today. The vast majority of the population were farmers, and so while a lot of farmers died, that also meant that there were fewer people to feed. The basic institutions of society — manors, courts, the Church — all survived. If soceity had collapsed completely, then there would have be no monks around to write about it all forty years later!

Quotes are from R. Horrox (ed.) The Black Death (Manchester, 1994) - a comprehensive collection of source material on all aspects of the plague.

Ormrod and Lindley (eds.) The Black Death in England (Stamford, 1996) has chapters covering pretty much everything if you want to know more.