The most recent inspectors’ report for The RJ Mitchell Primary School in Essex, northeast of London, says it has slightly more pupils on free school meals — a measure of poverty — than average and that the students’ knowledge of other cultures is ‘under-developed’.

But the six and seven year olds sitting on the classroom carpet look scrubbed, neat and healthy — and are engrossed in a Mandarin lesson.

As they rush through personal pronouns and numbers from one to five, I have difficulty keeping up. The children then stand up to ask each other’s names in Mandarin. Two boys get permission to show off and also say: ‘Hello, how are you?’

I was invited to the school after I wrote about the call by David Cameron, the UK prime minister, for British children to ditch French and German and learn Mandarin instead.

Several UK private schools already offer Mandarin. Wellington College in Berkshire has a Mandarin language centre housed in a pagoda with a Chinese water garden.

But Dragons in Europe, which, with Cambridge University Press, publishes Mandarin teaching materials, asked whether I wanted to see what a state primary was doing.

Barry Read, RJ Mitchell’s head teacher, says he welcomed the inspectors’ call for wider cultural engagement (the rest of the report described the school as ‘good’). The local area, he says, can be inward-looking. There has been ill-feeling between a few of the English and Polish pupils, which he believes reflects what they have heard at home. Mandarin lessons are part of an effort to get students to engage with the world.

The school will not forget its British roots. It was built on an old Royal Air Force base from which pilots flew during both world wars. The school takes its name from Reginald Mitchell, creator of the Spitfire fighter aircraft. The classrooms are named after RAF pilots, including two Polish airmen. One of the school’s exhibits is the nose of an unexploded German bomb that fell on the area.

The school’s decision to offer Mandarin classes to some of its youngest pupils — those in their second and third years — is interesting. Some researchers have argued that young children are particularly receptive to new languages and that their capacity declines gradually until puberty, after which learning becomes much more difficult.

The debate is usefully summarised by David Singleton, fellow emeritus of Trinity College Dublin, in his paper “The Critical Period Hypothesis: A coat of many colours.”

Examining how children and adults succeed in transferring speech from damaged parts of the brain to healthy ones after injury, one researcher argues the results show that “the human brain becomes progressively stiff and rigid after the age of nine” and “when languages are taken up for the first time in the second decade of life, it is difficult . . . to achieve a good result”.

Some argue that language learning declines for social reasons, that children acquire a firmer sense of who they are as they grow older and become embarrassed about acquiring another linguistic identity.

Others say that while younger learners have better pronunciation, they do not necessarily acquire a surer command of a new language.

Mr Read believes, however, that his older students are more inhibited about language learning and, watching the enthusiasm of his younger charges, it is hard to argue.

The parents need no persuading. “I think it’s fantastic. In years to come, Mandarin is going to become so widely used,” says Mandy Taylor, one of the mothers. Her son Mason greets me confidently in Mandarin and draws the Chinese character for ‘small, in my notebook.

The bigger question is whether the school and the children can sustain this.

Stephanie Driscoll and Ruthie Davies, their teachers, are sharp and engaging, but do not speak Mandarin. They are staying a step ahead of their pupils.

If Mandarin is to become a world language, it needs a huge corps of teachers, as English has — not just native speakers but foreigners trained in it. If China wants to extend its influence and culture, its ‘soft power’, it should train hundreds of thousands of teachers.

Young Mandarin learners, with their interest in a new culture and language, may start asking how free their Chinese counterparts are to question their leaders or to use the internet, but that is the scrutiny that comes with being a great power.