"She pointed at the entrance of a Woolworth's shop"
A Woolworth's shop
Creative Commons Attribution Share AlikeA Woolworth's shop - Credit: Jonathan Billinger

Woolworth’s was a chain of stores founded by American Frank Woolworth.  They had a strong high street presence in the UK from 1909 until their liquidation one hundred years later. 

Although the demise of Woolworth’s did not occur until three years after the publication of Never Let Me Go, the fact that the chain is now defunct adds to the nostalgic quality of Ishiguro’s narrative.