I can only really talk about paganism within the Roman Empire up to the seventh century, and even so it is more of a deconstruction of your question than a comprehensive answer, but I hope it will still be useful/interesting!

Essentially, Christianisation took a very long time to happen, even in the Roman Empire, so plenty of people continued to be 'pagans' (it is worth discussing exactly what this term means, since it can be a very vague term, but here I'll just use it to refer to non-Christians) for a very long time. Even worse for anyone interested in a firm answer, 'Christian' is also a very vague term. Our literary sources are almost uniformly written by educated wealthy urban Christians, so it sounds like there was a pretty firm idea about what being Christian meant - in reality, no such luck. Based on the archaeological evidence, it would appear that plenty of people were okay with syncretism, the mixing of different beliefs together. For example, both 'Christians' and 'pagans' used curse tablets to plea for divine justice, whilst in a sixth-century church in Jordan you can literally find figures from pagan mythology on its walls; the congregation was presumably Christian, but cultural paganism, if I'm allowed to make up a term on the fly, was very much a thing. To be honest, I'm not sure if the change to a Christian empire meant too much for most people, as the Christianisation of the empire was slow and inconsistent, Was there an hegemonic Christian culture replacing the Romans' pagan past? I don't think so, as the picture is most likely a lot of more complicated than that, to the extent that it might be best to say that the same old Roman traditions continued, albeit framed in a different way, though this is just personal speculation based on my interpretation of the material.

Of course, we do have mentions of pagans in literary sources, many of them in fact, but there are a few problems with them. Some of our best sources for the Roman Empire in the sixth century, such as Zosimus and John Lydus, were most likely pagans, whilst the even more important Procopius was a possible pagan. These men were not just country bumpkins either, but important men in their own right. Both Zosimus and John Lydus worked for the Constantinoplitan bureaucracy and even the praetorian prefect who oversaw the building of famous Hagia Sophia may be a pagan. An important religious leader of the time, Severus of Antioch, was a pagan in his youth in the late fifth century, but he converted and then went on to become the patriarch of Antioch and the intellectual founder of the miaphysite church, which is I think a pretty clear demonstration of how complicated this world was. Other examples can be found from records of how hard the state had to try to clamp down on the pagans - the Neoplatonic academy in Athens was closed under Justinian in the early sixth century, but it returned a few years later (we don't know what happened after that), whilst a campaign to convert the pagans of Asia Minor allegedly yielded tens of thousands of converts. Near the end of the century, a large group of pagans were discovered in Antioch and hauled of to trial to Constantinople. Indeed, for centuries afterwards, pagan-istic behaviour was consistently recorded in ecclesiastical/hagiographical sources across Europe, so a strong case can be made that paganism of all sorts continued to survive throughout the early middle ages.

However, whilst it is possible that real pagans were indeed running around the countryside doing pagan-ish things, it is I think more likely that they were simply doing what they and their family have always done whilst still believing in Christian doctrines, following rituals and traditions that defied simple categorisation. They might see themselves as Christians and the local bishop might see them as pagans, but who were they really? These categories were all rather fluid and we shouldn't see them as in opposition to each other. In some cases, people did not have to hide their paganism at all. In the late fifth century for example the ascension of Clovis as the king of the Salian Franks was welcomed by Bishop Remigius of Rheims, who saw him as a protector of the Christian flock. The two seemingly formed a lasting friendship, one that eventually culminated in Clovis' conversion to Christianity, but it is at least clear that in the early years a pagan elite essentially ruled a Christian Gallo-Roman polity with the help of local bishops.

I'm saying this because although people's beliefs in late antiquity and the early middle ages are fascinating, there is also a lot we don't know and I think firm answers about paganism dying out at a certain time are not possible. So instead of doing that I wrote about how this model does not work, which make this more of a non-answer to be honest, but hopefully someone will find it interesting nonetheless.

Follow up question to this. Is there any evidence of small groups of Pagans remaining in England after it became fully Christianised? Or would these groups have been quickly flushed out?

During Charlemagne's time there is a very big push to convert the Saxons to Christianity. Charlemagne essentially is at war with them for around 30 years and when he finally conquers them he attempts to force them to convert, and ends up killing a pretty substantial number who either refuse or go back on their conversion. There are several documents that seem to keep some of the names of these pagan gods, but one thing thats useful to keep in mind is that often the only record we have of some of these comes from a Christian perspective. Sometimes they would translate the names of pagan gods into more familiar Greco-Roman ones. One such document is the "List of Superstitions and Pagan Practices" which despite the promising name, is not quite a simple list. The problem being that the title was given to it later, and its actual usage and meaning is a little bit more complex. (I don't have the translation in front of me but where its contained in its manuscript it seems to have more to do with a list of things people should not say than what someone observed somewhere) Because the sources have many problems when dealing with pagans, its difficult to get at how widespread these religions may have been Also, from the late 600s throughout the 750s and onwards there is a pretty strong missionary contingent that comes to the continent (some come from England and Ireland). So at least in the period 760-800 or so there are still pagans in Europe (I'm fairly certain it lasts longer in Saxony too, but by the 900s its pretty Christianized). So thats a pretty basic answer for a time period from roughly 700-840 or so. Hopefully that helps! Also if you are looking for that document above you can find an English translation in Carolingian Civilization: A Reader by Paul Dutton. Also some other reading that might be interesting, is James Palmer's Anglo-Saxons in a Frankish World which deals with the missionaries quite a bit, although his focus is more on how they provided useful narratives for later hagiographers. I can almost guarantee there are other books on paganism in the Carolingian world, but thats not quite my specialty so I don't have more to offer.