There are currently 100 names on a waiting list to get into one of the existing three Hampton primary schools, head of schools infrastructure Brian Howard said, and he told city councillors that there is no answer to fixing that problem.
He added: “We are full in every year group in all three schools.”
Other pressure points in the city for places include Woodston, Fletton, Stanground, Helpston and Eye.
Hampton remains a fast growing part of the city with four villages being built east of the A15, near Teardrop Lake, as part of the Hampton East project.
Lynne Ayres, council cabinet member for education, skills and university, said: “We have now started analysis to find a solution to easing the pressures caused by an increased number of families moving to the Hampton area.
“The new Hampton East development will contribute an additional 3,000 units, including two primary schools, both with two forms of entry (i.e. 60 places per year group).
“The first of these schools, Hampton Lakes, is due to open in September 2019 with two forms of entry into reception year. The second primary school could open from September 2021, subject to the progress with the ongoing housing development.”
Moreover, the council is warning that the number of school places in Peterborough could reach “critical” levels by 2020. It is hoped the Government will sign off on a new secondary free school at Paston Reserve to ease the pressure, but if not introducing bulge classes - which are an additional class to what the school normally takes - are one of the contingency options.