Not a large number of women writers from working-class backgrounds are associated with this kind of literature, although three who are have roots in the Manchester area: Ethel Carnie Holdsworth, Ellen Wilkinson, and Shelagh Delaney (1938–2011), from Salford.
Interestingly, the naturalistic content of the play wasn't dissimilar to Delaney's reading: the likes of Zola and the Goncourt brothers. And there was a different French connection that the press played with: at nineteen, Delaney was the same age as Françoise Sagan had been when her Bonjour Tristesse (1954) had exploded on the reading public, so inevitably Delaney was hailed 'the English Sagan'.
ADDENDUM: I forgot to mention that – in a seriously delayed volte-face – Salford announced last month that November 25 (Delaney's birthday) will be Shelagh Delaney Day!
A brief interview clip:
Shelagh Delaney in 1959