The premises on Cole Road was in lockdown for most of the day yesterday after the incident.
Co-headteacher Mike Pearse said: "We believe the man accessed the school by a temporary fence which was in place because of works to our water system.
"The individual was not known to the school.
"He was up on the roof for five hours and while up there he did cause some damage - just by walking on them probably makes them looser.
"We called the emergency services immediately and the school was put in lockdown.
"The pupils were kept inside, the blinds were pulled down and in some cases we moved the children into different classrooms.
"We would like to reassure people that this individual did not get into the school building at all - the site was secure at all times."
Mr Pearse also praised Thames Valley Police for their quick reaction to the incident.
He said: "The police were fantastic - they were at the premises on mass within minutes and managed the situation.
"We had five or six police vehicles and senior officers at the scene.
"Our initial aim was to safeguard the children and secure the site.
"We informed parents as soon as possible - but some rumours were already circulating on social media by that time.
"We spoke to the children to reassure them but it is a credit to the calm way that the staff dealt with the situation that a lot of the children did not know what had happened at the end of the school day."