Early Christianity in Britain
The best general book about the development of Insular Christianity is Michelle P. Brown, "How Christianity Came to Britain and Ireland." It is scholarly, readable and beautifully illustrated. There is a review of this in Glastonbury Review 114. Be cautious about books which refer to 'the Celtic Church' as if it was a distinct denomination. Whilst there were undoubtedly Celtic churches they were very much part of the wider Christian world.
Charles Thomas, "Christianity in Roman Britain to AD 500" (1981) and Louis Gougaud, "Christianity in Celtic Lands" (1932) are sound and scholarly. Barbara Yorke, "The Conversion of Britain 600-800" deals with a later stage in the conversion but is sound and up to date scholarship (reviewed in GR 115) . Jacob G. Ghazarian, "The Mediterranean Legacy in Early Celtic Christianity" is not as crazy as its subtitle "A journey from Armenia to Ireland" makes it sound and has some interesting views (reviewed in GR 117).