Erskine May (first edn 1844) became the classic authority, the current edition is now made available online and open access
Essays on the History of Parliamentary Procedure by 
Bills and Acts : legislative procedure in eighteenth-century England by 
Justice and Grace : private petitioning and the English parliament in the late Middle Ages by Rotuli Parliamentorum
Parliamentary records begin to survive in significant measure from the late thirteenth century - but consistent survival was still a century away. By the 1340s a standard format of opening speech and sermon, any grant of taxation, the common petitions and the king’s answers, the statutes brought in. "The parliament rolls are generally a record of the conclusions of the assembly, rather than indicating the process by which those conclusions were reached, and they are often rather coy in recording anything that might indicate major political conflict." Paul Seaward, Subject guide: parliamentary history on British History Online https://www.british-history.ac.uk/using-bho/parliamentary-guide
See further general introduction below:
The Parliament Rolls of Medieval England, 1275-1504 by 
Parliamentary Texts of the Later Middle Ages by 
Proceedings in the Parliaments of Elizabeth I by NB Mirror of Parliament (January 1828–October 1841) was a weekly record of debates in both Houses which employed reporters trained in shorthand to record at first hand, something which Hansard did not do until 1878. Gladstone is recorded as having said: ‘I do not hesitate to say that Barrow's Mirror of Parliament is the primary record, and not Hansard's Debates, because of the great fullness which Barrow aimed at and obtained’ (Hansard, 233: 1577; 20 April 1877). K Chittick, 'Mirror of Parliament" in The Oxford Reader's Companion to Dickens (OUP, 1999) available in the EFL.
Advance search SOLO for the journal Mirror of Parliament and you will find open access routes to digitised scans of the volumes.
"Hansard" is being used here as shorthand to include Cobbett's Parliamentary History (Hansard before Hansard). It is Hansard is report of what is said in Parliament at Westminster. With improving techniques for recording it has become a “substantially verbatim” record.
The Bodleian Law Library has a near complete run on open shelf. The Law Library doesn't have a copy of volume 274, 5th series of House of Lords (1956/7) nor a copy of volume 351, 5th series of House of Commons (1939). Both are available free online Lords v. 274 and Commons v.351 (There is a print copy of the latter in the old Bod.)
The volumes in the Law Library, for both House of Lords and House of Commons, are on open shelf on Level 0, the ground floor.
"While Cobbett had the foresight to initiate these important publications, Hansard had the determination and industry to continue their production on a regular basis. John Wright, who worked for both Cobbett and Hansard on the parliamentary series, was noted for his indolence, and the main burden of the work fell on Hansard, whose Parliamentary Debates was soon recognized as the standard record."
(see David Lewis Jones, ‘Hansard, Thomas Curson (1776–1833)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Jan 2008 [http://www.oxforddnb.com/view/article/12222, accessed 14 April 2014]
Cobbett's Parliamentary History
The Parliamentary Debates First Series
The Parliamentary Debates Second Series
The Parliamentary Debates Third Series
NB Mirror of Parliament (January 1828–October 1841) was a weekly record of debates in both Houses which employed reporters trained in shorthand to record at first hand, something which Hansard did not do until 1878. Gladstone is recorded as having said: ‘I do not hesitate to say that Barrow's Mirror of Parliament is the primary record, and not Hansard's Debates, because of the great fullness which Barrow aimed at and obtained’ (Hansard, 233: 1577; 20 April 1877). K Chittick, 'Mirror of Parliament" in The Oxford Reader's Companion to Dickens (OUP, 1999) available in the EFL. Advance search SOLO for the journal Mirror of Parliament and you will find open access routes to digitised scans of the volumes.
The Parliamentary Debates Authorised Version Fourth Series
Official Report Parliamentary Debates Fifth Series
The Parliamentary Debates Sixth Series
The English Parliament in the Middle Ages by 
Law-Making and Society in Late Elizabethan England by 
Parliaments and Politics During the Cromwellian Protectorate by If the Bodleian Libraries don't have the book you are looking for, we may be able to source it through Oxford's inter-library request service.
