Be careful to disambiguate from the BBC Symphony Chorus, both have used the name BBC Chorus at different periods of their histories.
"Wireless Singers" was the name of an octet subset formed in 1927 from members of the Wireless Chorus, so it existed contemporaneously with the larger chorus group until 1934. when the group was renamed the BBC Singers in 1934, it was reorganized into two octets known as Singers A and Singers B, differentiated by their repertoire.
In 1961, Peter Gellhorn took over the choir. He re-organised the professional contingent, scrapping the A-B division in favour of a single force of 28 voices, which was renamed the "BBC Chorus". Following the appointment of John Poole as chorus master in 1972, the choir reverted to its previous name, the "BBC Singers".