Not aĺl of the extra places will be the result of immigration.
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Of course not, however it is probably the biggest reason:
http://www.telegraph.co.uk/education/educationnews/11083683/OECD-UK-class-sizes-among-biggest-in-developed-world.html
From link:
The disclosure will raise concerns that a rise in the birth rate combined with the effects of immigration may be placing huge pressure on schools. Experts have claimed that large classes can hamper children's education because they receive less one-to-one attention.
Elsewhere:
http://www.dailymail.co.uk/debate/article-2660839/NORMAN-LAMONT-The-people-spoken-mass-immigration-So-political-class-hear-them.html
From link:
For a start, many Britons, and particularly those who would traditionally be described as working class, find themselves excluded from the labour market.
In addition, the sheer scale of immigration is having a dramatic effect on the size of our population, which in turn is increasing the burden on our infrastructure.
If the influx continues at its present level, at least ten million people will be added to the population over the next 20 years.
Even now, our civic infrastructure is badly over-stretched, as reflected in the pressure on GP practices, transport, housing and schools.
Based on their own experiences, the public instinctively understand this.
They also grasp that this situation has been created partly by our membership of the EU.
Sounds about right to me!