Hi,
There is a Gladys Littlejohn on the midlands electoral roll living at 31 Porchester Street, Lozells Ward (includes Handsworth I think)in 1930.
Others at that address are Emily, Arthur and William Richard Littlejohn.
In 1925 it was just Arthur and Emily Littlejohn but Gladys may not have been old enouh to vote.
Do those names ring a bell.
Of course if it is her then the address may not have been where Joan was born, could have been in hospital, probably only a birth certificate would tell you..