There was an infirmary attached to the Workhouse in Toxteth Park. My GG Grandfather's death certificate states that he died in the Workhouse Infirmary in 1915, of valvular disease of heart, aortic. He was living in South Hill Road, when he was admitted as a patient.
I think that the Workhouse and Infirmary became Sefton General Hospital, and is now the Asda superstore. Hope this helps.
troymantis