I think the answer is a qualified no. The thing about land ownership is that it often tends to come into question when there's a massive political upheaval. Many invasions and/or civil wars tend to completely displace the prior elites and install new ones. Revolutions might destroy an elite altogether. Although there's been a couple of dynasty changes and definitely some civil wars, England is fairly remarkable for having a political system (used loosely) which is more or less continuous since 1066. Few countries in the world have gone that long without a major revolution of some kind that completely upended the system and displaced the elites.
Since we're talking about the Norman invasion, thinking about what happened to Saxon elites after the invasion is probably instructive. Even those who survived the war would likely have lost all their landholdings. You're very unlikely to find a whole society of elite families that have managed to hold on to land (or wealth) for a period of time much longer than 1000 years.
However, there are some things we can still pick out as individual examples. Family estates or family businesses that have lasted that long or longer. Italy and France have a few notable examples of estates that survived their respective political upheavals. These are notable precisely because of their rarity. They also aren't precisely the estates of nobility, but are slightly smaller in scale. Family property holdings and businesses that have survived through the centuries.
Chateau Goulaine in Haute Goulaine france is a family owned vinyard that has been owned by the Goulane family since approximately 1000 AD. Several other french wine estates can trace their roots back to the monarchy, most have changed hands on several occasions though.
the Pontifica Fonderia Marinelli is a Bell Foundry in Agnone Italy. It is considered the oldest family business in Italy, having been founded in 1040 AD. It still sits on the current site that started as its manufacturing site in 1339. The Marinelli family are at this point approximately 20th generation bell makers, and still run the business.
Similarly, Barovier and Toso are italian glassmakers just outside of Venice, operate a family owned company that was founded approximately 1200 AD, and has operated in primarily the same location for most of their history, with the family having 21 generations of glass makers.
There are also a significant number of very old family companies and estates in Japan, including Hoshi Ryokan, an inn in Komatsu that purportedly dates to 718 and has been run by the same family for that time period.
Edit: Although I've not looked into the age of church properties, as someone else mentioned that's also very plausibly within the scope of OP's question. Many church holdings and sacred sites in the Catholic, Orthdox, and likely Buddhist churches date quite far back. The oldest I've personally been to is the Cathedral of St. Sophia in Novgorod which was built in 1045. It's remained within the ownership of the Russian Orthdox church since that time period.(more or less, the church itself has had some major changes) I've never been to Rome or Istanbul, both both cities contain older church buildings as well.
I wonder if any Vatican experts could chime in as to the oldest land in the church's possession? That's got to be a couple hundred if not a thousand years old.
Could someone please also elaborate on the descendent of the Norman invasion that OP mentions?
Late to the party, but here's my two cents. I think it's best to look at small families, like another poster noted, powerful families have more to lose during upheavals.
That being said, a good example could be a family that isn't small at all: the Visconti, lords of Milan from the 13th to the 15th century, (and active in Lombard communal politics since the 10th century). They claim to have been landholders in Massino on the shores of lake Garda since the land was granted to them in Roman times; indeed they claim descent through the Roman era from Eneas, the ancient Trojan hero (mind sources on this are questionable and propagandistic, many conveniently having appeared when a match was being made between Gian Galeazzo Visconti and Isabel of Valois, daughter of the King of France. The most complete chronicle was written in the 14th century by the Milanese chronicler Galvano Fiamma, who spends a great deal of time on the Visconti's great exploits in his Politia Novella, or modern history of Milan, today stored in the Ambrosian Library. The tone he takes when speaking of the Visconti is unsurprising given he was Giovanni Visconti's personal chaplain).
Although the main Visconti line died out in the 15th century (and the throne passed to the Sforza, which could be considered a cadet branch but should really not be) a couple of cadet branches continued to exist in obscurity as small landholders in the Lombard countryside. Many were involved in business and real estate in North Italy up to modern times, the most easily traceable being the line of the Visconti of Modone, descendant of Vercellino Visconti, younger brother of Matteo Visconti (1250-1322) who was the Duke of Milan from 1294 to his death (with an eight year-exile after the Della Torre seized back the lordship, but that's beyond the point). The family was clever with their allegiance even after the throne of Milan slipped from their family, and several members were modestly important diplomats and civil servants in the court of the Sforza. They were elevated to Dukes by Napoleon himself in the early 19th century. The family count among their number Lucchino Visconti (1906-1976) and his brother Erpirando Visconti (1932-1995), both successful film directors. I reported initially that this was the last branch of the Visconti to go extinct, but I just checked and it turns out I was wrong; Erpirando does have descendants, they live in a modest villa near Bologna. It appears they do not own any more land near Modone, but have significant wealth managed privately.
Another cool example are the Obertenghi, who descend from Boniface, a Bavarian ennobled with significant lands in Northern Italy by Charlemagne (he was granted nearly all of modern Tuscany, Emilia, Lombardy, Peidmont and Liguria). The Obertenghi saw their lands reduced to Lombardy and Emilia by the eleventh century, and finally split into three cadet branches by the twelfth century: the Estensi, Pallavicini, and Malaspina, all three mildly influential during the communal era, and increasingly obscure when the communes were consolidated into the dozen Italian states of the renaissance. The Estensi, who became lords of Ferrara, are the most illustrious and are related to nearly every royal house in Europe, they were the first to go extinct. The Malaspina, the Tuscan branch of the Obertenghi, were Marquis of Massa-Carrara, but had their holdings progressively reduced under the Florentine Republic and subsequent Grand Duchy of Tuscany. They split into various branches living along the Tuscan-Ligurian border and as far as I know they all went extinct (although I don't know as much as I'd like on Tuscan history). The last branch are the ones who answer your question: the Pallavicini, already active in Emilia and Lombardy in the communal era, became powerful vassals of the Duke of Parma, but wisely allowed themselves to slip into obscurity during the Italian Wars. To this day there is a Milanese and Emilian (based in the town of Zibellio) branch still in existence, both are active in real estate in the Emilia-Romagna region.
I could also add a section on Venetian Families; however because of the way Venice developed, true Venetian patricians seldom hold landed titles, and thus do not pertain to your question. That being said, I'd like to mention the Dandolo, a family that gave the Republic of Venice four Doges. A branch of them is still extant today and inhabits one of their original palaces along the Grand Canal in Venice. The Dandolo family traces their lineage back to the roman gens Ursia, who arrived in Venice in the eighth century from the Pentapolis (the last five Roman cities to be abandoned by the withdrawing Byzantine empire). However, I am not sure they still hold the deed to the palaces previously owned by the family. I know of two; one is a hotel, the other holds Venice's city hall.
Edit: Cleaned up my wall of text, added sources for the Visconti, and fact-checked some things that were bothering me.
Alright maybe this isnt what you are looking for so someone please correct me.
One of the longest Chinese family line you can trace back is Confucius's line. His current descendent still holds a ceremonial title in Republic of China (Taiwan). His family tree is well documented.
Throughout the different dynasties, the head of the Kong family was also revered as its own noble.
Their ancestral home is listed in the UNESCO but I guess you can say they are still the landholder of the land.
Mods, let me know if i should put more sources in and I will.
From about year 40BCE to 1935CE, the heirs (from 13th generation to 77th) of Confucius had nobility titles in China, and their family residence in QuFu next to the Confucius temple had been in the same place, that's the only Chinese example I can think of.
UNESCO page about the residence/temple and nearby cemetery:
What about the japanese imperial family?
According to James Lees-Milne in the Burke's Genealogical and Heraldic History of the Landed Gentry, three families in England can be identified with confidence that can trace its lineage in the male line back to pre conquest times. They are the Arden family from Warwickshire ( William Shakespeare's mother Jane Arden is a famous example), the Berkeley Family from Gloucestershire and the Swinton family from Northumberland and Scotland. King Cerdic of Wessex is also claimed to be an ancestor of Elizabeth II. Although I do not have the book, as volume 1 is from 1965, you can still access it via various genealogy and library databases.
Source: Burkes Genealogical and Heraldic History of the Landed Gentry, 18th edition. Volume 1.London, England: Burke's Peerage Ltd, 1965-1972 )
Edit: Source and some words
Link to where you read about it? Sounds interesting.