Katrina,
Going on the "within the smell of the sauce factory" clue and it only being called the Eagle I would guess it to be the Eagle Inn Park Road Aston which was close by the HP sauce factory. Here is a photo, see if it raises any memory.
Hi MikeThey now seem to be on the online electoral roll after 1955 (possibly you looked some time ago before the site expanded their dates). 1955-1960 they are at 61 Inkerman st. then in 1962-65 they are at 49b Wickham House. Great Lister St. The online roll goes to 1965 now.