Well beyond the fact that any sort of "secret society" is well, by definition, secret and not liable to be reflected in sources, what are we left with?

Certainly anxieties about relapses into paganism, and incomplete devotion to God, were very much on the minds of Christian intellectuals in the immediate aftermath of conversion in England. The process itself took nearly a century to complete and there were of course residual holdovers of pre-conversion society. Now these holdovers can be broadly divided into two categories. Those that were overlooked or more broadly tolerated and those that were not.

Certain practices were just not compatible with Christian life and needed to be changed or eliminated in order to preserve the souls of the English. One of these practices was the consumption of horse meat, invariably in sacrifical contexts, though this later became horse meat in general.

I've written on this topic before, but I'll copy the relevant parts below.

During the conversion process to Christianity, among the practices that were outlawed or at least very harshly condemned, was the practice of horse consumption. Robin Fleming's Britain After Rome mentions this in the context of Anglo-Saxon England, but it was also present in Scandinavia and on the continent. The relationship between Germanic pagan religious life and horse meat did not escape the notice of Christian authorities. As a part of St. Boniface's mission in Germany, he was instructed by the Papacy to stamp out the practice of horse consumption as a pagan and abominable practice that had no place in Christian society. ...

Poole makes the argument that horse meat was consumed almost exclusively in pagan sacrifices and this association between paganism and horse meat was too strong for contemporary Christians to look the other way on. He examined the relative levels of horse remains that are believed to have been consumed in England in three time periods. The levels of horse remains in each time period is rare, but much more pronounced in the Early period of Anglo-Saxon England (c500-700), pre-conversion. It then collapses quite dramatically in the middle period (c700-900), and finally concludes with a slight uptick in the Late Anglo-Saxon period (900-1100), however it does not become nearly as well represented it was in the earlier sites. The connection between horse meat and pagan sacrifice is further born out in other contexts as well such as Iceland.

There are other practices, in different, but related, cultural contexts such as Scandinavia, that were strenuously suppressed such as infant exposure. Practices such as these were deemed incompatible with Christian life and severe penalties were ascribed to continuing to practice them.

Other practices were not so strenuously suppressed. The Venerable Bede for example mentions amulet wearing remaining popular among the people as a defense against diseases. Now according to Christian doctrine all sorts of magical protection were at best ineffective, at worse the works of evil powers. This did not stop their popularity and their use among the general public, and it must be understood that to these people it is unlikely amulet wearing was deemed as incompatible with their relatively new Christian faith. Other practices such as leaving out small offerings of grain to local spirits also survived in a relatively tolerated state of being.

Now these two categories of beliefs are important. To Christian authorities, the first signified continued pagan allegiance and the latter did not, and by the time of the Viking incursions, there is quite frankly, no evidence for the continuation for these more "pagan" practices on a scale to make plausible the existence of continuous of pagan communities. These other less "pagan" activities, while vexing to Christian authorities, did not signify continued pagan allegiance and were allowed a certain degree of toleration.

As evidenced by the eradication of horse consumption in Anglo-Saxon England, practices that showed allegiance to pagan beliefs were swept away by the sea of conversions int he 7th century. It was another nearly two centuries until the Norsemen showed up and while it is possible that some remote areas of England maintained some sort of veneration for the old Anglo-Saxon gods, it is really quite difficult to entertain seriously. Such communities are even more problematic to imagine having survived when you look at examples of some of the remaining pagan hold outs and their eventual fates.

The last remaining pagan Anglo-Saxon kingdom in England, on the Isle of Wight was, according to the Venerable Bede, utterly eradicated and its king, his brothers, and the people killed and the land taken over by the kingdom of Wessex. While obviously an extreme example, and unusual in the context of Bede's account, it seems clear that there was little room for both religious traditions to share.

Given such examples of what happened to remaining pagan communities, it is hard to posit that other communities survived, given the hostility from Christian authorities, both in the Church and in the "state".

Now what about after the Norsemen showed up. It is difficult for a number of reasons to ascribe pagan practices, no matter what contemporary sources say, to the English living under Danelaw. Partly this is due to the speed with which the Danes took to Christianity in England. However, even in the short while the Norse remained pagan in England it is unlikely they encountered any long lost Anglo-Saxon communities that retained their pre-Christian faith.

To add a bit to u/Steelcan909's excellent, comprehensive answer:

A lot depends on what you mean by a pagan religion. In 10th century England, people believed in elves and used magic to cure the diseases they believed the elves caused in livestock and humans. When beer brews turned sour, they used magical charms to fix the brews. We know this because Christian monks recorded, and recommended, these magical beliefs and practices.

Do the examples above count as paganism or not? Elves are obviously not something you get from the Christian scriptures--they come from Northern European pre-Christian beliefs, ie "paganism." But English Christians--including those with education--didn't see all of these pre-Christian beliefs as incompatible with their Christian faith, and they actively incorporated many into Christian practices. Sometimes this was deliberate: Pope Gregory the Great famously told St. Augustine (the Christian monk from Rome often credited as converting Kent to Christianity c. 600) to "borrow" pagan holidays, temples, etc to make Christianity more familiar / palatable to the people he was trying to convert. Often, however, it was just because medieval people didn't see these pre-Christian beliefs as being necessarily incompatible with Christianity. So what if elves were a pagan idea--they were just another kind of supernatural enemy that good Christians could fight off with prayer and appropriate rituals, right?

I like to draw an analogy with modern science today--most modern Christians don't have a problem believing in both miracles and science at the same time. Similarly, a lot of "paganism" was fine in early medieval England (so long as you weren't eating a horse or doing one of the other things that had been singled out as too pagan, often by churchmen who thereby sought to draw a line in the sand to remind everyone that they controlled religious power by prescribing certain behaviors).

A Scandinavian invader might have been able to sit down with a Christian Englishman and share stories about the Aesir and the elves, and if they kept talking they might have discovered that their mothers shared a few similar beliefs about the kinds of everyday magic you needed to use to keep a household running. But that doesn't mean they would have considered themselves to share the same religion.

Karen Jolly's book, Popular religion in late Saxon England: Elf charms in context, is great if you want to dig deeper into anything above.