Ms Hillier became the borough's mayor following the May local elections. It is a crucial position because Islington is now hung, with Labour and the Liberal Democrats holding 26 seats each.
In her article (LGC, 12 June), Ms Hillier promised to be a 'people's mayor' who would hold borough-wide surgeries.
But one Labour member, who refused to be named, told the Islington Gazette: 'She talks and behaves as if she's the leader of the council . . . She is getting incredibly big for her boots.'