Antibodies are produced when naive B cells differentiate into plasma cells within germinal centres (GCs) of lymphoid tissues. Patients with B cell lymphoma on effective immunotherapies exhibit diminished antibody production, leading to higher infection rates and reduced vaccine efficacy, even after B cell recovery. Current ex vivo models fail to sustain long-term GC reactions and effectively test B cell responses. Here we developed synthetic hydrogels mimicking the lymphoid tissue microenvironment, enabling human GCs from tonsils and peripheral blood mononuclear cell-derived B cells. Immune organoids derived from peripheral blood mononuclear cells maintain GC B cells and plasma cells longer than tonsil-derived ones and exhibit unique B cell programming, including GC compartments, somatic hypermutation, immunoglobulin class switching and B cell clones. Chemical inhibition of transcriptional and epigenetic processes enhances plasma cell formation. While integrating polarized CXCL12 protein in a lymphoid organ-on-chip modulates GC responses in healthy donor B cells, it fails with B cells derived from patients with lymphoma. Our system allows rapid, controlled modelling of immune responses and B cell disorders.