Our understanding of how much of the area was devastated rests on chronicle evidence – which records that William "utterly ravaged" the north as punishment for its disloyalty to him – study of settlement patterns (which, it has been suggested, imply the laying out of "new villages" from scratch some time after 1069) and an examination of Domesday Book, which suggests that the damage stretched from Cheshire to Northumbria, but was worst in Yorkshire and Durham, where large areas that had been under cultivation in 1066 were recorded to be "waste" in 1086 – which certainly seems to imply they were economically unproductive. Some entries in Domesday Book imply land values in Yorkshire fell by 66% between 1066 and 1086 and more than half the villages in the county were listed as partially or totally "waste" in 1086.

Orderic Vitalis, writing some time after the fact (c.1125) from a monastery in Normandy, is the source for the frequently-cited, but implausible and unproveable, statistic that "more than 100,000 Christian folk of both sexes, young and old alike, perished of hunger." Symeon of Durham, who was on the spot but writing in c.1129, adds that much land remained uninhabited nine years later and that "between York and Durham no village was inhabited." And William of Malmesbury – another late, southern author, but the most respected historian of the age – summed things up by saying that land was left untilled "over more than 60 miles" and remained uncultivated at the time he wrote, which was 55 years later.

Nonetheless, Palliser, in the most detailed recent re-examination of the evidence of Domesday Book, points out that the great survey is at its least convincing and least accurate in Yorkshire and adds that it does not pinpoint exactly when or why the "waste" areas it records ceased to be farmed. Land listed as "waste" can be shown, on occasion, to have been at least partially populated and partially farmed, and Palliser adds that many of the worst affected areas don't correspond too well to the routes William's armies are generally presumed to have taken.

In addition, the area was certainly fought over in 1066, while the border areas to the north that also suffered greatly were subject to repeated Scottish invasion (especially in 1070) and border raids, and the whole of the north was later prepared for the possibility of Danish invasion in 1085, which Kapelle suggests might also have involved some destruction of property associated with Norman counter-invasion forces living off the land. It's also been suggested that the word "waste" may have meant simply land from yielded no tax income – for what might have been a variety of reasons - rather than "ravaged land". All this led the historian Paul Dalton to conclude that there are "logical grounds for doubting the equation of waste with physical destruction and for disposing of the myth that the Conqueror organized a systematic devastation of the north."

Palliser's conclusions are as follows:

It would be wrong to conclude that William's punitive actions in 1069-70 were not catastrophic. The chroniclers may have amplified and exaggerated the atrocity stories they took over from the lost sources on which they drew. but it was clearly a harrying which shocked men of the twelfth century and struck them as beyond normal or acceptable limits. Maitland's sober conclusion was that 'William's deliberate devastation of the north is but one final and grandiose exploit of an ancient kind of warfare. After his day agrarian history becomes more stable because invasions cease and the character of civil warfare changes'. There is nothing wrong with that judgement except for his ignoring the savage warfare of the Anarchy of Stephen's reign. Both in the 1140s, and to a lesser extent in the revolt of 1173-74, there is also good evidence of destruction of crops and other assets, though in both cases recovery was swift once disorder ceased... These twelfth-century events, like experiences of later and better recorded warfare, are a reminder that wide areas can be dreadfully ravaged, and yet can recover fairly quickly. It is not necessary to assume that, even if Yorkshire was severely ravaged in 1069-70, the effects would still be acutely visible in 1086--88.

He adds:

"Doubtless there was much death, destruction and emigration; but it is scarcely credible that large parts of Yorkshire - or for that matter the whole area between York and Durham, as Symeon alleged - could really have been left without a single inhabitant for twenty years. If that had been so, it is curious that so many local men so quickly re-emerged in the records. For instance, ten York moneyers, all with Scandinavian names, coined for William I’s second issue type; only one coined Type III, probably because there was no business during the revolt and the Harrying, rather than because they had vanished, since five out of the ten reappeared on William's later coins. Likewise, recent research is finding more English thegns and lords who managed to keep possession of their Yorkshire lands until 1086 and on into the twelfth century ...

"A final point that might be made is that the usual estimates of Yorkshire's population in 1086 are probably much too low. The total population recorded in the Yorkshire Domesday appears to be about 7,570, giving an average of under three inhabitants per square mile, and making it one of the least populated shires. However, Darby conceded in 1977 in presenting his Domesday population data that 'the picture that emerges is only a very imperfect one' ,and there can be little doubt that Yorkshire's statistics are more imperfect than most... In short, the totals that can be constructed for the population of Yorkshire from Domesday Book are of limited use; and they cannot be used to argue that the shire 'must have remained thinly populated for many generations after the devastation of 1069... If recent estimates now put the population of Roman Britain at its peak, and also of England around 1300, in the range 4 to 6 millions, then surely a higher rather than a lower Domesday figure is called for."

There's more in a helpful earlier thread discussing the Harrying of the North, led by u/Steelcan909, which can be read here.

Sources

William E. Kapelle, The Norman Conquest of the North: the Region and its Transformation, 1000-1135 (1979)

D.M. Palliser, "Domesday Book and the 'Harrying of the North'", Northern History 29 (1993)