On a damp Saturday morning in November a steady trickle of more than 50 older primary children cross the campus of Manchester University, enter the library, and go into a room set aside for their English class.

They warm up with some brain gym exercises led by Ruth Ibegbuna, a secondary English and drama teacher, then start examining a poem by Seamus Heaney with their class leader, primary head Carol Powell. Later they will split up for small group work, where the standard of work produced will be “amazing”, according to the four teachers running the class.

Lewis McKay, 11, says of the Saturday sessions: “They’re great. They get me out of the house, and I like writing. Everybody here does.” And, he says, it has helped with his schoolwork.

A few miles away, in a bright, new city technology centre next door to Parrs Wood high school, a class of gifted mathematicians are taking down their homework - is 2,743,921,786,420 divisible by 2, 3, 4, 5, 6, 8, 9, and 10? Meanwhile, at Oswald Road primary, drama students are animatedly working on a piece about the conquest of Mexico that they’ll perform at the city’s big annual arts festival.

All these classes are advanced learning centres, conceived by the National Primary Trust as a way of offering talented and gifted children the chance to be stretched and challenged in out-of-school classes. Started in Birmingham, they have spread out under the umbrella of the Excellence in Cities programme.

Accelerated learning is, itself, accelerating fast in Manchester. Last school year the city ran a maths programme. This year it has two centres for English, one for maths, and the drama programme, which it is developing as a national pilot. Eventually, says Richard Fye, Manchester’s Excellence in Cities primary co-ordinator, it hopes to have classes in ICT, art, philosophy and science.

The small number of primaries involved are bursting at the seams. The centres cost about pound;40,000 a year to run, with a unit cost of about pound;200 per pupil and with teachers paid a generous pound;30 an hour.

They are open to students working at level 5 or above, or whose teachers believe they may be suitable. The demand is there: children from all racial and social backgrounds come from miles around, and arrive whatever the weather. The Saturday classes stretch them academically but also introduce them to places like the university, and get them used to working alongside other smart kids.

Nationally, 22 centres are up and running, about two-thirds of them teaching maths. The rest offer English, with science, art, German and ICT also being piloted, along with Manchester’s drama centre.

The NPT estimates that a centre with two or three teachers and 24 pupils can cost less than pound;10,000 a year to run. With demand outstripping supply, the trust envisages local authorities and school consortiums starting their own centres.

Ones to watch

Brunel University Runs gifted and able programme

Warwick Site of National Academy for Gifted and Talented Youth

National Primary Trust Started the ball rolling