Who led the Viking conquests of the British Isles in 865, and who were the major Viking players?

All of what we call England today would not fall under complete dominion of Norse rulers until the 1000s, and at various stages the other modern nations of the British Isles were fragmented into smaller kingdoms and fell into and out of Norse hands at intervals. But the most serious attempts at conquest certainly got under way with the arrival of the so-called 'Great Heathen Army' on East Anglian shores in 865.

The legend has always gone that after Aella of Northumbria had Ragnar Lothbrok killed, Ragnar's sons came back to the British Isles to avenge him. All of that is hard to prove. What we know is that the titular leaders of the invasion were men called Ivar (the Boneless), Ubbe, and Halfdan. All were said to be sons of Ragnar. Can't prove that. But the Anglo-Saxon Chronicle, various Sagas, Saxo Grammaticus and Asser have referred to those three men. As befits viking practice of the day, there would have been many other/lesser chieftains who also took part. A defining characteristic of the Norse raids was that consolidation of power was a prickly issue, and if a particular leader did not like the way a plan was being mapped out, or a feud arose between he and another chief, he would leave and take his oath-men wherever he so chose.

Other names of so-called kings, earls and lords who are recorded as having taken a leading role in the initial wave of assaults include Bagsecg, Sidrac, Oscetel, Anwend, and Guthrum. It's interesting to note that some of the vikings' leading men were largely only referenced at all because they were known to have been killed in battle - Sidroc is a primary example of this. So there were clearly other leaders who went unnamed by the sources, and unfortunately we'll never know their names. One must keep in mind that the Saxons themselves often learned the names of viking leaders only during parlays between the sides, upon prisoner exchanges, and the like. Guthrum is known for far more, including that he became a king of East Anglia after his conversion to Christianity, but that's another tale

Ivar is best-known for being the supposed progenitor of the Ui Imair, House of Ivar, viking kings who ruled in Dublin, York and the Isle of Man and other smaller kingdoms in the cadet branches. What we know with certainty about his role is that he, along with Halfdan, arrived on the East Anglian coast in 865. They took large sections of the country, forced King Edmund of East Anglia into paying them tribute, and set up bases of operation in the kingdom from which they could launch raids into other parts of modern-day England. Some sources say that part of the tribute Ivar and Halfdan received from the king was a great number of horses, which were then used in 866 to raid north into Northumbria. They also simply took a great many horses to mount their raiding forces. Once in the north, Ivar and Halfdan captured York (Jorvik). They held the city against multiple attempts by the fractured Northumbrians to reclaim the city - the largest battle took place in 867. In 869, Ivar was said to be one of the leaders of viking forces who killed Edmund of East Anglia. Abbo of Fleury, Aelfric of Eynsham, and others don't exactly agree upon the nature of Edmund's death, but the story generally goes that the vikings shot him full of arrows after Edmund attempted to convince them that by converting to Chrstianity they would earn God's immaculate protection. Ivar disappears from the sources in the early 870s; two Anglo-Saxon chronicles give his death in 870, while the Annals of Ulster list it as 873.

Halfdan's name appears most often as a leader of the early 'Horde' clashes between Anglo-Saxon and viking forces, and yet his history is muddled. It was said by the Anglo-Saxon chronicle that he helped lead viking forces at Ashdown, Reading, and York. He helped Ivar establish a puppet Anglo-Saxon leadership in York, and I can't remember for sure which source said it but he supposedly stayed in York during the first two winters of viking dominion and ruled from behind the throne of puppet 'king' Ecgbehrt. After the vikings suffered a rough defeat at Ashdown in 871, he ruled viking London (coins from this time bearing his image have been found). He was also king in York briefly, after returning north in 874 and 875. Asser details his forays north from York into Scotland against the Picts and the Kingdom of Strathclyde. He is said to have died on campaign in 877.

There is little known for sure of Bagsecg. He was said to have led a large Norse fleet to aid the Great Army in 871, and his force has been dubbed the 'Great Summer Army'. He was killed at Ashdown, a major viking defeat after the consolidated forces attempted to strike into Wessex.

In the 'History of St Cuthbert', Ubbe is referred to as a lord of the Frisians. In other sources, he's described as a Danish earl and one of the sons of Ragnar. He helped Halfdan and Ivar to capture East Anglia, was involved in the conquest of York. It's said he played a leading role when Aella and Osbhert, the deposed Anglo-Saxon rival contenders for Northumbria's throne, attempted to take back the city. Ubbe is said to have then struck south, into Mercia, and taken Nottingham. Which leads us to your follow-up question...

...In early 868, Mercian King Burhred and Aethelred I of Wessex (Alfred the Great's brother) joined forces to try and force the vikings out of Nottingham. Nottingham being a key inland route for viking ships, the Anglo-Saxon kings realized their danger. If allowed to mass troops so far inland, the viking raiders could coordinate better-informed, larger and more destructive forays into the Mercian and West Saxon heartlands. The two kings laid siege to Nottingham, but it was largely said to have ended in failure. While the vikings did leave Nottingham for a time, they also exacted tribute from the Anglo-Saxons to add to the goods, slaves and treasure taken from the Mercian countryside they overran on the way to Nottingham. So that's 1 and 1/2 instances of Anglo-Saxons uniting against the vikings; first the Northumbrian lords, then Mercia and Wessex.

In 874, however, the vikings overran Mercia and forced Burghred and the royal family into exile. They then installed a man called Ceolwulf (thought to descend from the royal family of Hwicce, a client kingdom of Mercia). So Northumbria, East Anglia, and Mercia were all under viking control. That left nobody for Wessex to ally themselves with. Alfred the Great eventually fought his way back from exile in the marshes of Somerset. He not only expelled the vikings from Wessex but, by virtue of his politic, appointments, and alliances with the new rulers of Mecia and East Anglia, managed to bring other Anglo-Saxon warbands under his banner to combat the vikings in later years. So the various Anglo-Saxon realms did unite against the viking invaders, but there was a lot of fracturing and re-configuring of the kingdoms even as the viking army churned across the Midlands and southern England. But that's a longer story than I have room to tell right now.

Sources - don't have page numbers in front of me, but passages from the Anglo-Saxon chronicle contributes a lot to my memory (not so much the 'avenging angels and heavenly fire' parts, but, yeah...), also Asser's 'Life of King Alfred'. Also the Saga of Ragnar's Sons has a lot of hard-to-verify but tantalizing stories. I also remember Kevin Crossley-Holland's 'Anthology of the Anglo-Saxon world' was good, it included some good stuff about Ashdown and Alfred's relationship with Guthrum/Aethelstan, a bunch of interesting fragments and passages from West Saxon law and poetry, etc. This post has gotten long and I really hope it gives you some insights/answers your questions.

This MAP is handy for visualizing the waves of viking raids, and this WIKI article has some pretty good info as well.

edits: spelling and linkage