Marsh says school insurance premiums will rise by 20%, because pupils are becoming increasingly aware of making claims for injuries sustained on school premises.
However, Britain's biggest school insurer, Zurich Municipal, said that claim was wide of the mark.
A spokesman for the company said: “Our experience, as the largest insurer of local education authorities in the UK, has not led us to conclude that liability claims are a sufficient issue to force the average level of premiums up by as much as 20%.”
Zurich agreed education was a growth area for liability claims and said there were a number of contributory factors, such as the Woolf reforms and the introduction of conditional fee arrangements (CFAs).
It said the range of issues had also been extended by rulings such as the Phelps case, where a former pupil won damages against the London Borough of Hillingdon for her dyslexia not being picked up by an educational psychologist.
Zurich said it was promoting risk management in schools to reduce the risk of incidents leading to claims.
Currently, more than 500,000 children every year are taken to hospital after accidents at school, with one third of these happening on sports fields.