A store person is a member of the art department who is in charge of receiving and dispatching deliveries. They are the lead at the studio's warehouse, or "stores". Although the position was only credited from A Christmas Carol through the conclusion of series 6 — and on Invasion of the Bane — the function of the position has been required since the beginning of the series in 1963.
In the first three decades of Doctor Who television production, the position would have been filled by someone working for the BBC, generally, and therefore wouldn't have been specifically credited on Doctor Who.