The question is an excellent one, and pre-Celtic society in Britain and Ireland is compelling and mysterious topic. However, with no intent to discourage you, what period is under discussion becomes an issue, as the question presumes a fixed Celtic 'arrival' in Britain, which seems unlikely to have occurred. A somewhat related question was asked previously: "Did the Celtic peoples "arrive" in Britain, or did Celtic culture just spread to the bronze-age inhabitants of the island?", in which /u/amusiclistener addresses some of the misconceptions surrounding Celtic languages in Britain and Ireland. I've also covered some subjects relating to Celtic languages previously:
Without entirely retreading those topics, the abbreviated summary is that if any migration to Ireland and Britain occurred, it would have been one of language rather than populations. The inhabitants of these islands are most closely related, in a genetic sense, to the prior inhabitants in any given period. Further, it is increasingly unclear whether the Celtic languages themselves migrated to the Insular world from a theoretical continental heartland, or arose in the Atlantic zone through sea-faring trade, small-scale settlement, and cultural and religious exchange. Also unclear is when this may have occurred. Although the habit in common parlance has been to vaguely indicate towards twenty-five centuries prior to modernity, it was likely to have been earlier, though how much is in open debate. This topic, and the hypothesis of Atlantic development is covered in exhaustive detail in the three volumes of Barry Cunliffe and John Koch's Celtic from the West (2010, 2013, 2016).
In this context, an answer to the question of what were the religious beliefs in Britain prior to either the arrival or development of Celtic languages will then vary depending on what period we wish (possibly arbitrarily) to regard as the T=0 of 'Celtic'; with correspondingly lesser evidence the further one ventures from the written historical record. Even later Celtic-speaking societies, which had the benefit of literacy, did not document pre-Christian belief and practice in anything but the most fragmentary way.
Without the benefit of literacy, the only attestation of pre-Celtic religious practice lay in the archaeological record, which is not well suited to preserve features as ephemeral as belief. While sites such as Avebury and Stonehenge have been extensively studied,^† our certainty about their purpose has actually diminished over time, and what can be inferred from these or other sites (such as countless barrows, passage tombs, tumuli, votive offerings, henges and much else) is at best highly speculative; speaking to what was done, but not necessarily why.
A related question such as What evidence survives of religious practices in Neolithic Britain? might be another avenue of inquiry, though it would be best answered by an archaeologist rather than a historian. In lieu of such a response, I would direct you to Ronald Hutton's Pagan Britain (2013) which is perhaps the definitive work on the subject.
^(† The first major scholarly study of these sites by the fascinating William Stukeley, who documented their purpose in vivid but perhaps, ahem, overly imaginative detail, permanently associating them with the Druids in the popular consciousness. His work, if not always credible, were a major contributor to the development of modern Celtic Studies and Archeology, as well as being in some sense the initiator of modern Druidic revivalism. For more on this subject, the excellent Blood and Mistletoe: The History of the Druids in Britain from Ronald Hutton.)