In this case, why would it put a child still at school as Bale(Allen) ??
Even though its not stated that Ada E is her mother ( as it never does in 1939)
Do I assume that Ada E was born a Bale but then married an Allen. But with her child being born a Bale and taken on the Allen surname. I suppose the child may have been born out of wedlock or her father died whilst she was young.
My guess would be the opposite of yours (ie. Lydia was born a Bale, named legally for the father, and Ava either returned to her maiden name after divorce -or- never married Ava’s father and no longer had any relationship after a time).
Check marriages on FreeBMD, Lydia Allen married Arthur Bale in 1950. The 1939 Register was used by the NHS services until about 1991. Look up ‘1939 Register’ on The National Archives website for a fuller explanation.
you will see that she was enumerated as Lydia I Allen (although the enumerator used ditto marks (shown under the “A” of Bale)). “BALE” was subsequently added when she married, the date of the marriage 17.8.50 being added to the address column with the initials REA. Her birth index record index would support that her mother was single (Dec 1928 Leicester 7a 405). Hope that helps.
I can’t really comment on the individual entry you’re asking about, but I can give you some background information which may be of interest. What you’re looking at is not the usual form of British census. The 1939 Register was instead created at short notice, and thus may not be quite so rigourous as would normally be the case.
On 1 September 1939 Hitler invaded Poland. Britain and France declared war on Germany two days later. On 5 September the National Registration Act was passed to allow the collection of information about civilians. Enumerators then visited every household in the country to collect names, addresses, marital status and other details of all civilians (military personnel were excluded) to help the Government respond to the emergency and coordinate the war effort at home.
The Register was used by the authorities for various purposes, such as enabling all civilians to be allocated a registration number and issued with wartime ID Cards. Incidentally, the same numbers were used again when the free National Health Service was set up across the UK in 1948.
Ongoing changes such as wartime volunteer duties eg : ARP (Air Raid Precautions) Warden and new surnames for women who later married were written in to keep it up to date - which helps to explain Charlie_Allingham’s comment above. This process continued until National Registration finally came to an end in 1952 (I was born in 1951 and still have my ID card).