No, they didn't, for a few reasons.
In the early parts of the Viking Age, in the Heptarchy (Northumbria, Mercia, East Anglia, Essex, Kent, Sussex, Wessex), there was nearly constant conflicts within and between individual kingdoms. In the 9th century, in the time of the so-called "Great Heathen Army", the kingdom of Northumbria was having some trouble. According to the Anglo-Saxon Chronicle "And there was much dissension in that nation among themselves; they had deposed their king Osbert, and had admitted Aella, who had no natural claim. Late in the year, however, they returned to their allegiance, and they were now fighting against the common enemy; having collected a vast force, with which they fought the army at York; and breaking open the town, some of them entered in. Then was there an immense slaughter of the Northumbrians, some within and some without; and both the kings were slain on the spot."
Earlier in the 9th century, Mercia and Wessex had been in conflict, and in the 830s Wessex appears to have been the most influential. At this time, while there are regular Viking raids, causing a lot of trouble, they are not recorded as staying overwinter in 854. Once the Vikings are regularly overwintering, they continue for a long time. While early medieval England became more centralized by the 11th century, the local eorls retained a lot of authority, and the responsibility to deal with raids. the king could raise a troop, but much of the burden fell on local lords, and therefore there was a lot of variability. Some lords found it easier to pay off the raiders, some consistently fought, and some allied with the Vikings! With such variability, leaving to attempt to raid Scandinavia (and these would be raids, not usurping the throne) would be risky at best.
Scandinavian people remained, mostly in Northumbria all through the 10th century, even after Æthelstan nominally eliminated the Vikings from England. Then, the second wave of raids starts at the end of that century, culminating in the 1016 coronation of Knutr as King of England. The divisions with Æthelred, and various earls choosing to side with the Vikings, ensured some problems.
One of the driving forces for the raids is the resource paucity in Scandinavia, particularly of precious metals. It's hardly the only reason, but it is one of them. England, as it turns out, does not have that paucity. So, there was frankly very little reason to chase a raiding band to Scandinavia; spending it on defensive measures like burhs or coastal navies is more important, and there are consistent records of kings after Ælfred doing exactly that. Additionally, paying things off via the proto-tax called the Danegeld proved to be a more efficient way of dealing with the Vikings, rather than trying to make it to Scandinavia to fight the various petty kings of the Viking Age (or, at the end of the period, the kings of Norway and Denmark).
Viking raiders were often small, independently-acting bands, hailing from all over Scandinavia. Attempting a military expedition would be an inefficient way to deal with these small raiding parties, that would not dissuade other raiders! It was better to deal with raiders as they appeared, or to pay them to settle and turn their deeds towards defending their new homes (as happened with Rollo the Walker being granted the title Duke of Normandy in 911).