The school building was opened in September 1860 and founded by the Church of England as three National Schools; one for infants, one for junior girls, and the third for junior boys. In the centre of the schools were two cottages, which were built for the head teachers of the three schools.

Girls and boys who did not pass the 'scholarship' remained here for the rest of their school career. Those who passed the scholarship went on to the Grammar School. During the 1930s the senior boys and girls left to attend the newly built secondary schools in London Road, and in 1939 this school became a primary school.

Andover Primary remains a Church of England foundation school. The parish church of St Mary’s retains a strong interest. The school is now maintained by the Local Education Authority.

Over the years many changes have taken place to this now Grade II listed building:

• Old classrooms have been converted into cloakrooms and a hall.
• The cottages have been integrated into the school linking the old, separated buildings.
• The heating has changed from open fires, to oil heaters and now modern gas and electric-fired systems.
• The school population has grown in size and for many years temporary classrooms were on the site.

During 2000 a major building programme took place; the temporary classrooms were eventually taken away and a new building, to match the old Victorian one was completed. This comprises 2 classrooms, to be used by Years 5 and 6, a computer suite, and extra cloakroom space. It was officially opened on September 27th 2000.