At the mention of Newbold my ears pricked up, as several generations of my family have been connected with Rochdale's Newbold Baptist Church since its innovation, including my great-grandfather, John Hurst. He did have connections with the Sunday School there, which was originally started for children who were working in the mills and could only get to school on a Sunday.
There is, however, a St Peter's C of E church and a primary school in the Newbold district of Rochdale of that name, so the photo could be showing children from that school, which was founded around 1870. The children certainly are looking smart. The Whit Walks would usually be the time for children to get new clothes.