Department for Education figures show 14 schools were at or over capacity in South Gloucestershire in the 2021-22 academic year.
Of them, 12 were primary schools and two were secondary schools.
A school is at or in excess of capacity when the number of pupils enrolled is greater than or equal to its number of places.
Jon Andrews, Education Policy Institute head of analysis, said the proportion of schools operating at over capacity is likely to fall in the coming years.
He warned the result of schools operating close to or over capacity is additional demands on teaching staff and pupils being left without their preferred choice of school.
He said: “With our research having revealed that pupils from more affluent backgrounds more frequently succeed via these routes of appeal, it’s likely that disadvantaged pupils will suffer to a greater extent from the effects of schools being over capacity.”
The figures show the most crowded primary school in South Gloucestershire last year was Lyde Green Primary School.
The school had 445 students on roll and 420 places – meaning it was over capacity by 6%.
The most crowded secondary school in the area was Digitech Studio School which had 527 pupils and 360 places last year. It was over capacity by 46%.
Geoff Barton, Association of School and College Leaders general secretary, said arrangements are put in place to accommodate pupils where a school is over-subscribed.
Mr Barton added: “The bigger issue is that this situation is often driven by Ofsted judgements rather than a shortage of school places in the system as a whole because many parents apply for schools with ‘good’ and ‘outstanding’ ratings.
“It drives up property prices in certain areas and stigmatises schools in other areas.”
He said the system “desperately” needs to be reviewed and added struggling schools need more support.”
A Department for Education spokesperson said it has created almost 1.2 million school places since 2010 and added many more are “in the pipeline”.
They said: “The vast majority of schools listed as overcapacity are either at or just over recorded capacity, and we work closely with local authorities to make sure they offer a school place to every child in country.”