When klasa-I put down their pens for lunch, their teacher, Kinga Wiśniewska, dashes downstairs to feed her six-month-old daughter. Her husband swaps their baby for supervising her class of 14 eight- and nine-year-olds and starts an impromptu maths lesson over breaktime.

The willingness of teachers to teach and pupils to learn when the rest of the country is out enjoying a sunny Saturday morning is striking, but this school, in a community centre in Ely, Cambridgeshire, is no ordinary operation. It is one of scores of Polish Saturday schools that have opened in towns and cities across Britain.

The schools teach Polish, as well as the history and geography of Poland, to the children. Most, but not all, of the parents are Polish. Ely’s school was founded by Wiśniewska and a friend in 2009 and this year has 52 children, up from 36 last year, including the daughter of a Thai couple who run a restaurant in Ely and want their child to learn Polish.

Wiśniewska’s school day begins shortly before 9am, when she drives into the front yard of the community centre in a minibus containing her three eldest children, who are 13, 10 and eight. The school is run by volunteers, who are parents of pupils. Wiśniewska works as a childminder during the week but, like all the school’s teachers, is a qualified teacher in Poland. Her colleague, Paulina Zakrzewska, was a teacher in Poland, but is now a waitress in a restaurant in Ely; she’s hoping to become a teaching assistant in a British school. “Lessons have to be interesting, because it’s their sixth day at school,” she says of her Saturday classes.

Wiśniewska’s children amuse themselves with a soft football while she dashes around with other volunteers, transforming the community centre into a school: heaving chairs, tables and whiteboards into six “classrooms” covering preschool and five age groups up to 13.

After the break, attention starts to wander ... Photograph: Alecsandra Raluca Drăgoi for the Guardian

Wiśniewska says she spends all her free time at home organising lesson plans, documentation and applications for financial support from the Polish government: “It’s hard work, but it makes me happy.”

Polish Saturday schools are thriving in this area: Cambridge’s has 200 pupils; Peterborough’s 500. They may be bigger than ever, but they are not new. One parent knows three generations of British Poles who have attended Saturday schools, which were first established after the second world war for the children of Polish soldiers unable to return to their homeland. Nowadays, the schools receive funding from a cultural institute for teaching Polish to expats in Britain and from Poland’s government for some building hire and book costs. This helps Ely’s school remain accessible for financially stretched families – it costs only £7 a child a day, with additional children half-price. Teachers are unpaid and any remaining funds are reinvested in books.

Lessons begin at 10am with Polish language, followed by an early packed lunch and then another lesson, alternately history and geography, before a 1pm finish. The preschoolers begin by making potato prints. Their teacher holds up paint bottles and asks the children to name the colours in Polish. Then they sing a Polish song that involves holding hands and falling down, much like Ring a Ring o’ Roses.

In Wiśniewska’s class, the children learn to read and pronounce basic Polish vocabulary. They read, spell and chant words with “a” sounds: aparat (camera), ananas (pineapple), waga (scales). When Wiśniewska points to a picture of a gooseberry in the Polish workbook, the children are stumped: like any child of 2016, gooseberries are not part of their everyday lives.

Children from preschool age to 13 attend the Ely school. Photograph: Alecsandra Raluca Drăgoi for the Guardian

Four of the boys in Wiśniewska’s class are new to the school and speak Polish, but cannot yet read or write in the language. This is common. Monika Bonczyk, who teaches the preschoolers, also brings her seven-year-old, Nicole; she speaks Polish fluently and, after starting Saturday school last year, can now read and write in Polish as well. “We’re just helping each other,” says Bonczyk.

“This is an additional day of learning, so we try not to be too strict with them,” says Wiśniewska. She says the first lesson is always fine, but after the break the children’s attention tends to wander. I spend break with a class who run around the sports hall, flicking off the lights and screaming with delight, but the pupils seem remarkably attentive again after the break.

“I remember when my kids started preschool aged three; they didn’t speak any English. It’s their main language now,” says Agnieszka Pekala, who has two sons and a daughter at the school. Like most parents, her children are usually alone or with one other British Pole in their UK classes, and they speak perfect, accentless English among their friends. “Our kids are five days at school. They speak Polish with us, but we can hear this accent – they speak Polish like a foreign person,” says Pekala. “Some Polish families’ kids speak in English at home, because they think in English. It’s very important for us [that they speak Polish], because they have to connect with grandparents and aunts and uncles.”

I hear no complaints about being dragged to school on a Saturday, but parents admit there is some reluctance. “There was a girl protesting this morning – she thinks her Saturday rights are being curtailed,” says Krystyna Bromek-Burnside, a parent-volunteer. “It’s a balance – you have to allow them enough freedom, because it’s the weekend. They have long school days, so you need them to do what they want to do.”

‘You have to allow them enough freedom.’ Photograph: Alecsandra Raluca Drăgoi for the Guardian

Bromek-Burnside’s seven-year-old son, Robert, “was reluctantly brought here – it wasn’t his idea to do it”, she says. Luckily, another group runs football training in the sports hall before lessons begin, and Bromek-Burnside, a physicist who works in IT, also offers a bribe: “Half an hour on the phone playing Pokémon Go. It’s amazingly effective.” Usually, when the pupils become teenagers, they choose to stop attending, but parents are trying to make it weekend-friendly. Because most junior football teams meet on Saturday mornings, a new team for Polish children has been set up in nearby Newmarket with games on a Sunday morning.

Most parental couples I meet are both Polish, but Bromek-Burnside’s husband is Scottish. Although he learned Polish, the couple speak English together at home. Their daughter was fluent in both languages when she was three – “she would stand between her two grandmothers and translate” – but Robert, their second child, was “far less immersed in Polish when he was little, and it makes a huge difference”.

Bromek-Burnside has noticed how the school now sustains Robert’s Polish. “He comes with new sentences, which we haven’t supplied,” she says. “It’s also a time for different friendships – they go to birthday parties of the children here.”

How does Saturday school compare with Monday-to-Friday school? “Better,” says Robert, “because I’m allowed to play football.” Is it hard learning Polish? “I’ve learned a few words,” says Robert. “You’ve learned quite a lot, actually,” says his mum.

After the EU referendum, there was a surge of parents who applied to become UK nationals, says Bromek-Burnside. Saturday school is a Brexit hedge for some: a key reason the Polish government part-funds these schools is so that returning expat children can slot into their year in a Polish school without too much trouble.

“I don’t know whether we will go back to Poland, because we have a home here,” says Wiśniewska, “but, if some day we do go back, it’s important for my children not to be way behind when we return to school there.”

Ely’s Saturday school seems to be a dedicated, supportive and friendly place. If being in a community hall is awkward, it also creates a more informal atmosphere than a conventional school. But, for all the pleasure the children take in each other’s company, school is school and children are children. When I ask Robert’s class what they like best about Saturday school, a girl shoots up her hand. “It’s shorter,” she says, laughing.