I really enjoy history that gets muddied by myth. I think that the period of England before and during the time of Alfred the Great is really interesting and I'd like to read a good book about it.
Also any early Irish history is of great interest to me as well.
Concerning England before the Norman Conquest, /u/BRIStoneman, /u/Steelcan909 and I posted some book lists for a while before in this subreddits:
As for pre-Norman Ireland, I'd recommend to check Clare Downham's Medieval Ireland, Cambridge: Cambridge UP, 2018, at first, since it offers balanced insights in the limited pages, and also covers Later medieval period a bit. Alternatively, the 2nd, expanded edition of the classic, Daibhi O Croinin, Early Medieval Ireland 400-1200, 2nd ed., London: Routledge, 2017 (1st ed. 1995), focuses more on pre-Norman Ireland in general.
Thomas Charles-Edwards (ed.), After Rome, Oxford: OUP, 2003, Short Oxford History of the British Isles 2, also provides us with the overview of the British Isles from the fifth to the eight centuries for beginners, covering both Great Britain and Ireland.