Much more can be said, but these answers on the conversion of Britons to Christianity ( u/Libertat) and its relation to [EDIT] Germanic settlers ( u/Steelcan909) might interest you, [EDIT] in the context of small-scale migrations

This is not a dumb question at all, in fact it's one that historians and archaeologists still puzzle over. By the time Roman rule in Britain came to an end, Christianity was well established as the state religion and persecutory laws against paganism had been enacted. The thing is, it's difficult to know how far these were enforced in a remote diocese such as Britain. Our only evidence of violent persecution of pagans is the damage done to all of Britain's Mithraic temples (the evidence is clearest at Carrawburgh). However, it is possible that this was due to Mithraism being an empire-wide semi-organised religion, popular with soldiers. So the authorities may have been much more lenient with localised, native belief. Evidence of Christianity itself meanwhile is also relatively elusive. It used to be thought that east-west orientation burials were evidence of Christianity, but it is now thought (see Petts, Christianity in Roman Britain) that the rite pre-dates widespread conversion, and appears to have been imposed by authorities rather than being a matter of personal belief.

Other archaeological evidence for Christianity is also quite limited. There are no certain examples of church buildings from Roman or post-Roman Britain, though there are several very good candidates. On the other hand, some pagan temples and shrines continued to be used possibly into the fifth century (see Dark, Civitas to Kingdom). Evidence of paganism among the elite drops off around this time, but there is also very little post-Roman evidence of Christianity. When in comes to the latter half of the fifth century, we also have very little archaeological evidence of Christianity or Romano-British paganism, in contrast to the Germanic paganism of the Anglo-Saxons, which has produced a lot more material. As such, we must rely primarily on written evidence. St Patrick, almost certainly writing at some point between 410 and 490, condemned a British ruler and his soldiers for killing and enslaving Irish Christians. Patrick was under the impression that these Britons were Christians themselves. Gildas, another British writer (probably living in the mid sixth century) condemns his people for their impiety, but nowhere does he mention British pagans. He also makes it clear that the kings of his day were all Christian, at least nominally.

So now to actually answer your question. In the early fifth century, as the first Anglo-Saxons were settling, there would have been a lot of British pagans around, possibly a majority of the population. By the mid sixth century however, when the settlement was still ongoing, relatively few Britons would have been pagan, and the ruling elite would have been entirely Christian. When the Anglo-Saxons converted is a little clearer. Augustine's mission began in 597 and over the course of the following century all of the Anglo-Saxon kingdoms were Christianised. Bede provides us with the details of this. However, we probably shouldn't simply accept Bede's claim that no Anglo-Saxons were converted before this. Bede was very Cambrophobic, and later Welsh sources contradict his claim that Britons did not evangelise amongst the Anglo-Saxons. Given that they were converting the Irish during this same period, it seems perfectly possible that some Anglo-Saxons were converted, by the Britons, before Augustine arrived from Rome. This, however, was probably on a small scale.