There are number of contemporary accounts that largely agree with one another and provide sufficient detail to locate the battle and produce a coherent narrative of its course. 

Contemporary Accounts                              

Sir Edward Walker, Historical Discourses on Several Occasions, London, 1705: Walker was the King’s Secretary of War and took part in the Newburycampaign, recording the meetings of the King’s Council of War, which he used in part to write his account of the battle.

Richard Symonds, Diary of the Marches of the Royal Army, (ed. C E Long), Cambridge, 1997: Symonds served as a trooper in the King’s Lifeguard of Horse in the campaign and had first had experience of the events he described.

Mercurius Aulicus week ending November 2, 1644:  The royalist news book published in Oxford and London provided an account of the battle, some of which is either taken from or used by Walker in his account. 

Sir Richard Bulstrode's Account (Sir Richard Bulstrode, Memoirs and Reflections Upon the Reign of King Charles I and King Charles II, London 1721, pp.117-119).  Bulstrode appears to have been acting in and aide de camp role to General Goring during the battle as Goring ordered him to bring up the Queen's regiment of horse which dealt with the Balfour's cavalry which penetrated on to Speenhamland. 

John Gwyn's Account (Peter Young and Norman Tucker (eds.),The Civil War: Richard Atkyns and John Gwyn, London, 1967 pp.58-62).  Gwyn provides a short and slightly confused account of the battle - he claims it was fought over the same ground as first Newbury in September 1643 - around Shaw House, presumably because he was on that side of the battlefield. 

John Rushworth, Historical Collections, (The Third Part, Volume the Second), London, 1691, pp.677-748.  Rushworth provides Major General Philip Skippon's account to the Committee of Both Kingdom's written on 30 October 1644, the Mercurius Aulicus  report as well as his own narrative.

Sir William Waller and Sir Arthur Haselrigg's letter to the Speaker of the House of Commons, (British Library MS Harley166 ff.139-140).  Waller and Haselrigg's account was written on 28 October.

John Crewe and Sir Archibald Johnston accounts (W D Hamilton (ed.), Calendar of State Papers Domestic 1644-45, London, 1890, pp.75-77.) Crewe and Johnston were the representatives of the Committee of Both Kingdoms and provided reports for the committee.

Colonel Richard Norton's account (Rev John Webb (ed.), Military Memoirs of Colonel John Birch, London 1873, p.215).  Norton's letter to Richard Major about the battle is short and focused on the action to take the royalists defences at Speen.  The letter corroborates other accounts of the fighting there.   

Edmund Ludlow account (C H Firth, The Memoirs of Edmund Ludlow, Oxford 1894, pp.102-104). Ludlow served with Manchester's forces at the battle and provides a more detailed account of the fighting around Shaw than the around Speen.  But the detail largely mirrors that provided by other writers. Blair Worden has raised questions about the authenticity of Ludlow's memoirs (Roundhead Reputations, London 2001), though this does not necessarily mean the detail of the account is incorrect. 

Samuel Bedford's note (H G Tibbutt (ed.) Sir Samuel Luke's Letter Books, Bedford, 1963, p.876.    Bedford was one of Sir Samuel Luke's men and his brief report from Waller's force on the western side of the battlefield provides useful detail on the formation of parliamentarian forces there.

British Library Additional MS 16,370 f.60, Bernard de Gomme's map of the royalists deployment at the 'third' battle of Newbury.

Secondary Sources

Walter Money, The First and Second Battles of Newbury,  London, 1884

Malcolm Wanklyn, Decisive Battles of the English Civil War, Barnsley, 2006

Chris Scott, The Battles of Newbury, Barnsley, 2008