• Details of the Register of Electors are held at the Bedford Record Office.
• For further reading about poll books there is Poll Books c1696-1872: A Directory to Holdings in Great Britain by Jeremy Gibson and Colin Rogers, published by the Federation of Family History Societies ISBN 1 872094 85 6.
• John Dawson has added transciptions to his web site for Poll Books of Bedfordshire 1722 and Poll Books of Bedfordshire 1784, both include indexes of names as well as the transcriptions.
• A list of the Bedfordshire Register of Electors, Poll Books and Absent Voters held by the Record Office.
• A list of Bedfordshire Poll Book Holdings are published here.
• A list of the Bedfordshire Register of Electors, Poll Books and Absent Voters held by the Record Office.
• A list of Bedfordshire Poll Book Holdings are published here.

In the UK these are referred to as Electoral Registers or Electoral Rolls. In earlier times they are often known as Poll Books.

• The electoralregisters.org.uk site offers ... information about the electoral registers, electoral rolls, poll books from 1700 to the present day, how to access the registers online, how to make the most from your searches, what is available and not available, and much, much, more.
• For some of the legal background, this legal volume about The Representation of the People Act, 1918 may prove useful - https://archive.org/details/representationof00frasrich?view=theater

• British Library holds copies of all past and present Electoral Registers for view by personal visit. Their online guide provides details of what is available, both from them and from companies offering paid-for online access. 
• Lists of Names: Pollbooks and Electoral Registers (archived copy), by Stuart A. Raymond.
• Electoral Registers - "information about the electoral registers, electoral rolls, poll books from 1700 to the present day, how to access the registers online, . . ."