A theoretical model of haemoglobin is presented to explain an anomalous cationic Hofmeister effect observed in protein aggregation. The model quantifies competing proposed mechanisms of non-electrostatic physisorption and chemisorption. Non-electrostatic physisorption is stronger for larger, more polarizable ions with a Hofmeister series Li+ > K+ > Cs+. Chemisorption at carboxylate groups is stronger for smaller kosmotropic ions, with the reverse series Li+ > K+ > Cs+. We assess aggregation using second virial coefficients calculated from theoretical protein-protein interaction energies. Taking Cs+ to not chemisorb, comparison with experiment yields mildly repulsive cation-carboxylate binding energies of 0.48 kBT for Li+ and 3.0 kBT for K+. Aggregation behaviour is predominantly controlled by short-range protein interactions. Overall, adsorption of the K+ ion in the middle of the Hofmeister series is stronger than ions at either extreme since it includes contributions from both physisorption and chemisorption. This results in stronger attractive forces and greater aggregation with K+, leading to the non-conventional Hofmeister series K+ > Cs+ ≈ Li+.