It's now possible to find all of the publicly available UK census records online. The records are generally released 100 years plus one after the event. Currently, England, Scotland and Wales have the years 1841–1921 available. Ireland has just released the 1926 records.
UK Census Websites
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Find My Past
FMP is my favourite for pretty much all UK genealogy records. Searching is easy and you get relevant matches to your queries. It's also possible to download images of census returns so you can save them on your computer for future reference. FMP has the England, Scotland & Wales census records from 1841–1901, plus England & Wales from 1911.
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Early British & Irish Census
The EBIC project brings the numerous disparate pre-1841 census records into one searchable database. The project offers valuable insight into household and occupational structures of early industrial Britain.
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Scotland's People
As far as I know, this is the only place you can search and view the complete 1841–1921 Scottish census online.
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Roots Ireland
Has some census and census substitute records.
1939 Register
The 1939 Register is now available. It provides valuable information about 41 million people living in England and Wales at the start of World War Two.
The 1939 Register is a fantastic resource for family history and social history research as it is the only surviving record of the population between 1921 and 1951. This is because the 1931 census was destroyed and one was not taken in 1941.
You can access the records as part of a subscription at Find My Past. It's also possible to buy credits to view the register. Search the 1939 Register
Free Census Records
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FreeCEN
Free. Includes records from 1841–1911 for England, Wales and Scotland.
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Census of Ireland 1901, 1911, 1926
The National Archives of Ireland have made the available censuses free of charge.
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Graham Maxwell
Some free Scottish censuses from 1841–1861.