Audrey Collins' blog post National registration day: 29 September 1939 says:
The completed household schedules were collected and returned to each
local National Registration Office, but they did not remain there.
Each person’s details were transferred to index cards, and the
original forms were sent to the local Food Office, for the preparation
of ration books. They were eventually reunited later in the war when
the National Registration Offices and Food Offices were combined.
An archived post (from nine years ago) from the newsgroup soc.genealogy.britain contains a summary of a communication received from ONS (Office for National Statistics):
We do not know whether households completed forms. If they did, then they are certainly no longer in existence.
What we do have is the Transcript Books which are the schedules (booklets) made up by the 1939 enumerators showing one line of
information for each person in the household.
We do NOT have index cards made up from the household forms.
What we do have is the A1 which is a card index originally made up from the information held at Local Registration Offices and sent to
Southport at the time National Registration ended in 1952. These cards
contained information relating to the whereabouts, name, etc, of
persons in 1952 which was not necessarily the same as in 1939 if they
had moved house, got married, etc. These cards were added to and/or
amended right up until 1991 in respect of persons born before 1952.
These documents are no longer held in the Ballroom at Smedley Hydro. Some are in the basement and some are on microfilm.
Further queries with regard the 1939 National Registration records
should be directed to the ONS Customer Contact Centre at
Ref: CCC84596 End of ONS message
I searched for research guides on the ONS site, similar to the ones ONS provides for historical census data, but so far I haven't found any.
According to Peter Calver's Lost Cousins Newsletter published 24 Aug 2015, the original forms haven't survived (he doesn't cite a source for that information).
The catalog description for General Register Office: National Registration: 1939 Register at TNA says:
For correspondence and papers on the administration of the 1939
Register, please see: RG 28
RG28 is General Register Office: National Registration: Correspondence and Papers
If there is a discussion about whether the original household schedules should be retained or destroyed, it might be somewhere in RG28.