In 1867 the school was housed in a building with 2 classrooms adjoining the church in Exeter Street. By 1871 there were 33 boys and 29 girls, paying between a penny and ninepence a week, and 29 free scholars. In 1886 there were 18 boys, 12 girls and 21 infants who were providing the main source of income for the school as state aid was not received until 1888. By 1890 there was a new classroom for infants and the total accommodation was 90 while by 1893 attendance had risen to 80 children. Alterations in 1895 increased accommodation to 118 but by 1902 there were 119 pupils and from then on attendances averaged between 120 and 140 until the early 1920s.
In 1924 the school transferred to better premises, 100 yards away in Exeter Street, at St. Elizabeth's, which had been used for the Certified Industrial School that had recently moved to Sheffield. The new building could take 100 mixed juniors and 60 infants in 4 classrooms. It was a 2 storey building in flint and stone with a brick extension. Between 1926 and 1937 the attendance averaged between 135 and 175 children. In 1944 the school was granted aided status and it remained an all age school until the early 1960s when a senior school, St. Joseph's Catholic School, was built while the juniors and infants remained at Exeter Street as St. Osmund's Catholic Primary School. St Osmund's expanded and most recently, in 1998/99, a new hall and 2 more classrooms were built while other facilities, including the library were improved. In 2002 there were 200 children, aged between 4 and 11 on the school roll.