For Northern Ireland, a free Freedom of Information request can be made to the Public Record Office of Northern Ireland (www.proni.gov.uk) for extracted details from the register; as it is catalogued by street address, you will need to know where your ancestors were on the night. For Scotland, for a fee of £15 you can access details for an individual (not a household) via www.nrscotland.gov.uk/statistics-and-data/nhs-central-register/about-the-register/1939-national-identity-register-and-how-to-order-an-official-extract.
Note that there was no 1941 census due to the war, so this makes a useful substitute. The 1931 Scottish census and the 1937 Northern Irish census will be published in due course, once 100 years has passed from their original recording, but there is no 1931 census for England and Wales (it was destroyed in the Second World War) - making the 1939 National Identity Register particularly useful for those two countries.
For the English and Welsh records, FindmyPast has a short background video on their conservation and digitisation at https://youtu.be/IdZE0NP-IVs - it is also presented here for convenience:
For details on my genealogy guide books, including my recently released Discover Irish Land Records and Down and Out in Scotland: Researching Ancestral Crisis, please visit http://britishgenes.blogspot.co.uk/p/my-books.html. My Pinterest account is at https://www.pinterest.com/chrismpaton/.