OK, so let's see where we are.
Mithraic border legions 'defect' to the barbarian kings that they are facing, bring their religion with them. In the East this has relatively little effect, but along the borders it has a big impact. Almost overnight the Empire is gone.
The wild barbarians take up the religion, attracted by bravery and military success of its adherents, and in the process Mithra absorbs some of Thor’s attributes, and Frejya some of the attribute of the Isis cult.
The religion also develops more grand public ceremonies to please the broad populace, but retains the mystery cult aspects for initiates.
One aspect of the broad adoption of Mithraism is that the german tribes become more disciplined in battle, beginning to actually listen to their generals and war leaders. As a result, more survive battle, thereby ensuring the expansion of the religion throughout Europe.
The more disciplined Goth Armies around the Black Sea are better able to resist the Huns, conquering them in battle several times. But news of the wealth associated with the Roman Empire reaches the leaders they determine to take advantage of the weakenss of the West by grabbing as much of it as they can. As a result they move west pretty much on the same time frame they did OTL.
The East Germans move into North Italy, pushing the Roman remnants, where they continue to practice Christianity, but North Italy becomes almost totally Germanic, particularly over the next hundred years as the Lombards move in.
Further to the North, the Franks gain the ascendancy, and to the West in Iberia, the Vandals now rule. All these tribes are Mithraic tribes.
Around 400-500 AD the British Isles come under the onslaught of the German tribes (Angles, Saxons Etc.), but unlike OTL, both the British and the Germans practice basically the same religion learned from the same source, the remaining legions. There are some differences however, the British Mithraism has also adopted some of the attributes of the native religions, in particular some practices associated with Druids.
Importantly, unlike in the rest of Europe, this Mitraism has undergone a sort of intellectual and philosophical transformation, introducing symbolic practices into the religion and abandoning the harsher elements of both druidic and german religious practices.
By 600, human sacrifice is gone as a central practice of any of the local flavors of Mithraism, and the British Isles have developed into a major center for learning and philosophy related to Mithraism.
One important aspect of Mithraism is the loyalty one owes one's War Leader. As a result, the Western political scene stabilizes earlier than in OTL into a sort of crude representative democracy. War bands but forth leaders in an area, extolling their virtues and bravery, and the only requirement is that you are a member of such a band who is above the initiate (“Friends”) level, during the ‘Althing’, a time set aside to settle disputes and lawsuits.
(Since Mithra is also a God of Law and Contracts,
However the final selection is performed by the Old Father, Mithraic warriors who are known for their virtue to Mithra, brave deeds and good works. Only after the Old Fathers have selected someone can that person be crowned King.