British and Irish Studies 

Mitchell, B. R. British historical statistics  Cambridge : Cambridge University Press, 1988 Perkins/Bostock Library Reference  HA1134 .M58 1988 
A standard reference book that gives the major economic and social statistical series for the British Isles from the earliest available, in the twelfth century, to 1980-81.

Office of National Statistics (National Statistics Online)
Free access to data produced by the Office for National Statistics, government departments and devolved administrations.

The portal to Ireland's official statistics.
Census Records in the National Archives
Records for  1841-1901 are online.
A Vision of Britain through Time
This site contains information about a local area from the 2001 census -- and from every earlier British census back to 1801. It can present this information both as maps of the whole country and as graphs showing change over time in a local area.
UK Data Archive
The UK Data Archive (UKDA) is an internationally-renowned centre of expertise in data acquisition, preservation, dissemination and promotion; is curator of the largest collection of digital data in the social sciences in the UK and houses a major collection of computerised historical material, including  AHDS History and the Economic and Social Data Series.
 Online Historical Population Reports
Also from the UKDA this collection provides online access to the complete British population reports for Britain and Ireland from 1801 to 1937.

NDAD: National Digital Archive of Datasets
 preserves and provides online access to archived digital datasets and documents from UK central government departments. spans 40 years of recent history, with the earliest available dataset dating back to about 1963.

Arts and Humanities Data Service
Digital resources for the Arts and Humanities.
What was the Exchange Rate Then? 
Find the exchange rate between the U.S. dollar and the British pound for any year between 1791 and 1999. (From Economic History Services).
Current Value of Old Money
Sources which attempt to answer the question "how much would a specified amount of money at a certain period of time be worth today?"
What was the UK GDP then?
Another useful service from Economic History Services.

Slave Movement during the Eighteenth and Nineteenth Centuries
Online data archive on the Atlantic Slave Trade.