Anti-cancer drugs, such as cisplatin and oxaliplatin, covalently bind to adjacent guanine bases in DNA to form intra-strand adducts. Differential recognition of drug–DNA adducts by the protein HMGB1a has been related to the differences in efficacy of these drugs in tumours. Additionally, the bases flanking the adduct (the sequence context) also have a marked effect on HMGB1a binding affinity. We perform atomistic molecular dynamics simulations of DNA with cisplatin and oxaliplatin adducts in four sequence contexts (AGGC, CGGA, TGGA and TGGT) in the absence and presence of HMGB1a. The structure of HMGB1a-bound drug–DNA molecules is independent of sequence and drug identity, confirming that differential recognition cannot be explained by the protein-bound structure. The differences in the static and conformational dynamics of the drug–DNA structures in the absence of the protein explain some but not all trends in differential binding affinity of HMGB1a. Since the minor groove width and helical bend of all drug–DNA molecules in the unbound state are lower than the protein-bound state, HMGB1a must actively deform the DNA during binding. The thermodynamic pathway between the unbound and protein-bound states could be an additional factor in the binding affinity of HMGB1a for drug–DNA adducts in various sequence contexts.