As family history enthusiasts, we get one of our best pictures of each family as the censuses are released for public use. We are still celebrating the release of the 1911 census and rejoicing in the information we are gleaning from its pages. At the same time, we are anxiously awaiting the release of the 1921 census around 2021.
Just beyond 2021, we are looking at a drought-filled 20 years without an England and Wales census as we know them. The 1931 census returns, including schedules, enumeration books and plans, were completely destroyed in a fire in Hayes, Middlesex, where the census was being stored. Many precautions had been taken to protect the census, which all failed. To read more about the 1931 census, see http://www.1911census.org.uk/1931.htm.
The 1941 UK census was not taken due to World War II. However, The National Registration Act, 1939, established a National Register “for the issue of identity cards.” This population count took place on 29 September 1939, and provided information for “all persons in the United Kingdom at the appointed time” and “all persons entering or born in the United Kingdom after that time.” The United Kingdom included England, Wales, Scotland, Northern Ireland, and the Isle of Man. Forty million people were registered in some 7,000 transcript books. (See the sample page below.) These provide a viable census substitute for the 1941 census. The schedule requested the following information: Name; Sex; Age (not year of birth); Occupation, Profession, trade or employment; Residence; Condition as to marriage; Membership of Naval, Military or Air Force Reserves or Auxiliary Forces or of Civil Defence Services or Reserves.
So, in answer to the title question, there are no censuses for 1931 or 1941, but all is not lost. There is a census substitute for 1941 that we will all learn to use and rely upon. For more information, see "Identity cards in Britain: past experience and policy implications," by John Agar.