The primary sources for the history of Anglo-Saxon England "from the time of the settlement of Germanic tribes in Britain until the accession of Edward the Confessor" are to be found in English Historical Documents c. 500-1042 edited by Dorothy Whitelock (2nd ed., 1979). Volume Two, which is edited by David Douglas and George Greenaway, provide material for the Battle of Hastings and later. As one can see from the copyright dates of the books below, this bibliography has become out of date over the past two decades, when it first was compiled.
Much of the literature and history of Anglo-Saxon England is available in paperback.
Tacitus: Agricola, Germany (1999) translated by A. R. Birley (Published in Oxford World's Classics, this new edition by a renowned scholar is preferable to the Penguin Classics text.)
The Anglo-Saxon Chronicle (1996) translated by Michael Swanton (Another newer translation that has taken the place of Garmonsway's translation in the Everyman Library.)
Bede: The Ecclesiastical History of the English People (1994) translated by Judith McClure and Roger Collins (The index and extensive notes, as well as the inclusion of supplemental material, including Bede's The Greater Chronicle, make this World's Classics edition a better choice than the more familiar Penguin Classics.)
Anglo-Saxon Poetry (1982) translated by S. A. J. Bradley (This anthology in Everyman is much more comprehensive than The Earliest English Poems in Penguin Classics.)
Anglo-Saxon Prose (1985) translated by Michael Swanton (A companion volume to Anglo-Saxon Poetry.)
The Age of Bede (1988) translated by J. F. Webb (Saints' lives, as well as The Voyage of St. Brendan.)
The Anglo-Saxon World: An Anthology (1984) translated by Kevin Crossley-Holland (Bits left out of the other World's Classics.)
Alfred the Great (1983) translated by Simon Keynes and Michael Lapidge (A thorough discussion of Asser's Life in Penguin Classics.)
Beowulf (2000) translated by Seamus Heaney (Winner of the Whitbread Award and recognized as an exceptional translation, although with little critical apparatus.)
Secondary sources are more varied but some general surveys are standard, both for the history and literature of the Anglo-Saxons.
The Blackwell Encyclopaedia of Anglo-Saxon England (1999) edited by Michael Lapidge, John Blair, Simon Keynes, and Donald Scragg
Anglo-Saxon England (1971) by Sir Frank Stenton
The Anglo-Saxons (1982) edited by James Campbell, Eric John, and Patrick Wormald
An Atlas of Anglo-Saxon England (1981) by David Hill
Anglo-Saxon England (1992) by Martin Welch (English Heritage)
A New Critical History of Old English Literature (1986) by Stanley B. Greenfield and Daniel G. Calder
The Cambridge Companion to Old English Literature (1991) edited by Malcolm Godden and Michael Lapidge
A History of Old English Literature (2002) by Michael Alexander
An Invitation to Old English and Anglo-Saxon England (1995) by Bruce Mitchell
A Guide to Old English (2001) by Bruce Mitchell and Fred C. Robinson
Britain in the First Millennium (2001) by Edward James
A number of primary sources have been made available in Oxford Medieval Texts, which offer both the Latin text and English translation on facing pages, as well as an extensive critical apparatus. In this series, the most important for the history of Anglo-Saxon England, especially the Battle of Hastings, are
The Chronicle of John of Worcester: Volume II, The Annals from 450 to 1066 (1995) edited by R.R. Darlington and P. McGurk
The Gesta Guillelmi of William of Poitiers (1998) edited by R. H. C. Davis and Marjorie Chibnall
The Carmen de Hastingae Proelio of Guy, Bishop of Amiens (1999) edited by Frank Barlow
The Gesta Normannorum Ducum of William of Jumièges, Orderic Vitalis, and Robert of Torigni (1992) edited by Elisabeth M. C. Van Houts
Henry, Archdeacon of Huntingdon: Historia Anglorum: The History of the English People (1996) edited by Diana Greenway
William of Malmesbury: Gesta Regum Anglorum: The History of the English Kings (1998) edited by R. A. B. Mynors, R. M. Thomson, and M. Winterbottom
The Life of King Edward Who Rests at Westminster, Attributed to a Monk of Saint-Bertin (1992) edited by Frank Barlow
The Ecclesiastical History of Orderic Vitalis (1980) edited by Marjorie Chibnall
Historical Writing in England c. 550 to c. 1307 (1974) by Antonia Gransden provides a satisfying overview of the historians of the period, beginning with Gildas and Nennius, Bede, and the Anglo-Saxon Chronicles, to mention the titles of the first three chapters.