In the autumn of that year 30 girls and 30 boys passed the 11 Plus and embarked on their secondary education at what was then the Aylesbury Technical High School.
The school moved to its Oxford Road premises in 1963 and the name was changed to the Sir Henry Floyd Grammar School two years later.
Sir Henry Floyd was a County Lieutenant from 1961 to 1968 and he opened the new school premises in 1963.
The school's first sixth form was formed from among the class of 58 who met for a reception and dinner at the Holiday Inn on October 20, organised by Ann Kibble.
The class of 58 has now passed retirement age and many are grandparents.
After leaving the school they embarked on a wide variety of careers in business and the public services, across the UK and overseas.
Colin Rickard, who attended the reunion and was a member of the class of 58 remembers the move to the new building.
He said: "The school’s move to Oxford Road gave it modern laboratories and much better on-site sports facilities.
"At its original location in Walton Road, daily assemblies were held in the Beaconsfield Road Guide Hall and reaching the main sports ground necessitated a cross country run along what was then a rural Turnfurlong!"
Speaking about the reunion event Colin added: "It was a very convivial and enjoyable event for all concerned."