The 1939 'Census' was taken in Sep 1939, using the stationery and admin framework that was already in place for the 1941 census, and it was used for National Registration, ie the issue of identity cards and ration books. Less information was gathered than in a normal decennial census, and after the war it formed the basis of the National Health Register.
In theory it should be available for release after 100 years (ish!), but I don't know whether this will be the case, because unlike a proper 'census', it was subsequently annotated throughout people's lives, so some of the information is relatively recent.
Mean_genie