The 1010s were an exceptionally eventful time in the history of England as a whole, for a number of reasons. The King at the beginning of the decade was Aethelred II, known infamously as Aethelred the Unready (which was actually an Old England play on words indicating that he was without good counsel). Aethelred was known for making poor decisions, and his policies against the Danes and other Scandinavian interlopers were notoriously ineffective for the most part. In 1010 English forces were defeated by Thorkell the Tall, a Viking invader who was supposedly a member of the semi-legendary Jomsviking group. His ravaging and plundering spread across East Anglia and Mercia (more or less contiguous with the modern day midlands) and he was eventually bought off with a very high danegeld, or ransom paid to convince him to cease his raiding. So, right off the bat if you were a resident of the areas he had raided you either were killed or might have had your estates attacked and possibly destroyed. In addition you might have been part of the forces sent against him and been killed. If you survived these ordeals then your lands were taxed heavily to pay for the hefty danegeld, which would be a significant part of your annual income. In fact, this was just one of the many reasons why Aethelred was unpopular.
Further battles occurred in the following years, with the introduction of a new heregeld tax which had the purpose of raising money to pay Anglo-Scandinavian mercenaries to fight off the Danes who were flocking to the country. At this point the Northern and Eastern parts of England were controlled by the Danes and called the "Danelaw," and the mercenaries were partly in place to prevent raids from this area as well. So on a national level the Danish incursions were a significant financial and military burden on southern English peasants and farmers at this time.
There were other invasions throughout the decade, culminating in the Danish King Canute (or Cnut) who unified England after the death of Edmund Ironside. Cnut was a great reformer who succeeded in unifying the two disparate parts of England in a more cohesive manner than previous rulers. So as an inhabitant of southern England you would in some ways have been drawn closer to your Northern relatives during this time. In addition you ended the decade with a foreign "viking" if you will as your King to whom you owed ultimate alliegance, which is about a great effect as you can think of. But don't fret - if you live until 1042 then you will have a King of your own people, as Aethelred's younger son Edward will come to the throne.
As you can see, the decade you selected experienced a vast amount of political and economic upheaval as a result of the Viking invasions, and in many ways this was the last of the successful tides of viking incursion. Conversion and assimilation were taking place in many areas of the Danelaw and also back in Scandinavia, and so the viking age was drawing to a close. in 50 years the Battle of Stamford Bridge would represent a definitive close to the heydey of Viking raids.
Sources: Lavelle, Ryan (2008). Aethelred II: King of the English. Stroud: The History Press.
Katie Wales, Northern English: A Social and Cultural History
Kendrick, T.D. (1930). A History of the Vikings.
Henry Loyn, The Vikings in Britain
Trow, M.J., Cnut: Emperor of the North