Type 2 diabetes (T2D) and hypertension increase the risk of cardiovascular diseases mediated by whole-body changes to metabolism, cardiovascular structure and haemodynamics. The haemodynamic changes related to hypertension and T2D are complex and subject-specific, however, and not fully understood. We aimed to investigate the haemodynamic mechanisms in T2D and hypertension by comparing the haemodynamics between healthy controls and subjects with T2D, hypertension, or both. For all subjects, we combined 4D flow magnetic resonance imaging data, brachial blood pressure and a cardiovascular mathematical model to create a comprehensive subject-specific analysis of central haemodynamics. When comparing the subject-specific haemodynamic parameters between the four groups, the predominant haemodynamic difference is impaired left ventricular relaxation in subjects with both T2D and hypertension compared to subjects with only T2D, only hypertension and controls. The impaired relaxation indicates that, in this cohort, the long-term changes in haemodynamic load of co-existing T2D and hypertension cause diastolic dysfunction demonstrable at rest, whereas either disease on its own does not. However, through subject-specific predictions of impaired relaxation, we show that altered relaxation alone is not enough to explain the subject-specific and group-related differences; instead, a combination of parameters is affected in T2D and hypertension. These results confirm previous studies that reported more adverse effects from the combination of T2D and hypertension compared to either disease on its own. Furthermore, this shows the potential of personalized cardiovascular models in providing haemodynamic mechanistic insights and subject-specific predictions that could aid in the understanding and treatment planning of patients with T2D and hypertension.