There is a lot we don't know about British Christianity. There are a couple of different readings on it; firstly that it was institutionally weak and relied on Imperial support (and thus largely collapsed after Roman withdrawal), or secondly that it was extremely strong and made a firm base for sending missionaries out beyond the boundaries of the Roman Empire to e.g. the areas now known as Ireland and Scotland. I tend towards the latter thought and that it heavily influenced insular Christianity, especially as I think there tends to be a neglect of pre-Augustine Christians who are very clearly present in the form of figures like St Patrick.

The earliest clearly datable evidence for Christianity in Britain comes from the council of Arles in 314, where we get the names of several British delegates including the Bishops of York and London. During the fourth century there’s clearly a Romano-British church with its own leadership and activity in larger church councils. The wall paintings at Lullingstone date from c. 350, although it’s possible that some of the earlier mosaics have crypto-christian messaging. Lullingstone is unusual for being one of the few. actual. visible. identifiable. worships spaces, and it is only evident because of the very unusual survival of the wall paintings. Trying to find public Roman churches in Britain is hell, and can be summed up as that meme of the dude and the butterfly, only the dude is labelled archaeologists and the butterfly is ‘is this an apse?’. We have a few strong other candidates, such as structures on the site of St Paul-in-the-Bail in Lincoln, but nothing with quite such strong evidence as Lullingstone.

We must remember that Britain was likely never fully 'Romanised', especially outside of urban areas, and that even within the elite Christianity was likely interpreted in ways related to their cultural background. British Christian worship seems to have been relatively unorthodox and seemed to draw heavily from pagan influences as well as being fairly gnostic and potentially heretical. For example, Pelagius was likely British or Irish, and although the actual details of his heretical views are quite boring to anyone who isn’t very interested in intense theological precision about the nature of sin he seems to have been quite popular in Britain. In 429 Germanus of Auxerre is sent to Britain in order to combat Pelagianism and is reportedly quite successful.

Some Romano-British Christians may have continued to make ritual deposits, as with the Water Newton hoard. Lullingstone itself seems to have maintained dual worship at the imperial cult in the cellar and the church above for some time, although what exactly this stand-off represents is unclear. It is possible that some family members converted and some didn’t or that their role - it may have been the home of the governor of Britain - meant they had to maintain worship related to the divine emperors. The situation around Christianity and paganism appears to be fairly complex and fluid, possibly with a pagan majority and a Romanised Christian elite.

Britain was, of course, ‘abandoned’ by the larger Empire sometime around the early 400s - the traditional date is 410 - and may not have been really subject to many of the prohibitions put upon pagans towards the late 300s. It is, after all, a long, long way from the metropole, and many of those prohibitions and arguments centred around worship in Rome with only a few scattershot attempts to enforce any laws outside of it. Britain itself was undergoing some big (although often infuriatingly vague) political upheavals and was increasingly cut off from Rome and Roman authority. If British authorities chose to enforce laws against public animal sacrifice, divination or apostasy, we don't hear of it - although we don't hear of very much related to Britain. It's quite likely that as in other parts of the Roman empire, the people in charge chose not to pick such an uphill battle.

Assuming that our Lullingstone family never converted and continued to celebrate various divine emperors on their estate, it is unlikely that they would have faced any legal consequences for it, especially as potentially the most powerful people in the area and as celebrants in an imperial cult. Even in Rome, private worship was not challenged to the same extent that public worship and public funding of that worship was, and many elites remained pagan well into the sixth century. The divine cult itself more transformed then disappeared. That said, although they may not have experienced official legal consequences, they may have experienced social consequences if the majority of their elite peers were Christian - those peers may have preferred for e.g. to marry someone who shared their religion - and it may have been easier to exert political power as a Christian.