The Bodleian Law Library has a near complete run on open shelf. ( We don'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 (for both House of Lords and House of Commons) are on open shelf on Floor 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
The Parliamentary Debates Authorised Version Fourth Series
Official Report Parliamentary Debates Fifth Series
The Parliamentary Debates Sixth Series
Please consult left hand box for a fuller description of these titles. It has to be said that - as of Jan 2016 - it is still often quicker to consult the print copy, rather than e-version ... if you have easy access to the LawBod that is!
Until this HL decision, legislative history was not a tool allowed the practising lawyer trying to establish intent/meaning of legislation.