Attending the memorial service, Chief Constable Sue Sim said of Pc Rathband: "He was gunned down in tragic circumstances doing the job of constable he loved.
"My heart goes out to Kath and the children and the rest of the family."
More top news
The singer, 31, said on Twitter that she and her partner Jonathan Powell were grieving their loss.
A fine evening ahead to the south with some late sunshine in places.
Prince Charles and the Duchess of Cornwall have visited Manchester Arena, the site of a suicide bombing in May which left 22 people dead.