Ok, I see how the unithistories site made the mistake. Eric was a cadet in the 40th Survey Training Regiment from which he was commissoned
The undermentioned, from R.A. (Cadets, 40th Survey Training Regiment), to be 2nd
Lts. 8th Mar. 1940: —
Charles William BRYANT (124825).
Arthur Cunningham PRIOR (124831).
Jocelyn Campbell KELSEY (124828).
William Ernest NOON (124830).
Ivan Neill TURNER (124837).
John William BRAILSFORD (124824).
James Eric GREENWOOD (124827).
Gilbert Hattersley KING (124829).
Richard Arthur RADFORD (124832).
Arthur Philip Heberden ROGERS (124833):
Leonard Chester SMITH (124834).
William Hammond SMITH (124835).
John WALMSLEY (124838).
Richard Fox (124826).
David John SCOTT (124836).