Christianity being perhaps the exception
Christianity effectively left with the Romans too. It was re-introduced to (what became) England via the Irish, Welsh and Scots - the Celtic church - before it came back into southern England from the continent. Without the Romans, there's a reasonable chance that Augustine isn't sent because Britain will still be seen as wholly barbarian, not an old province of the empire. There will still probably be a similar mission, but I think it would be later, resulting in more inroads being made by the Celtic church first.
Of course, the biggest problem both sets of missionaries (Celtic and Roman) would face would be the still-existing druidic religion. The two groups had different ways of dealing with the 'old religion', with the Celtic missionaries being more inclined to subvert it (in terms of taking people's old beliefs and practices, and turning them into Christian ways of doing things - even converting druids to Christian priests), whilst the Roman missionaries were more zealous, more inclined to just tell people that their old beliefs were wrong.
There were advantages and disadvantages to both ways of doing things. The 'subversion' method was generally quicker, but with more chance of people clinging on their old beliefs for more generations. The 'you're wrong, disown your old priests now' method faced more resistance initially, but once the old priests were gone, might be more solid. Of course, OTL the Roman missionaries never had to deal with the druids as the Romans (empire) had done that for them.
Getting back to the OP's question:
Yes, I think the Germanic invasions would still take place. They might even be more successful, as instead of facing a semi-organised land, they'd be facing multiple non-united tribes.
Sorry for the slightly rambling post - I was thinking as I typed!