Sepsis remains a leading cause of mortality in the United Kingdom, with approximately 245,000 cases identified annually and nearly 48,000 associated deaths, of which around 25% are considered preventable through timely diagnosis and appropriate intervention. Although sepsis is initiated by infection, disease progression is strongly associated with cardiovascular dysfunction, including myocardial depression and altered arterial haemodynamics. Electrocardiogram (ECG) abnormalities have been reported in a large number of patients diagnosed with sepsis, reflecting myocardial dysfunction through features such as reduced QRS amplitude and increased QRS duration. These ECG changes often precede overt haemodynamic instability, making ECG a valuable early-warning signal. However, ECG-based markers alone lack physiological specificity, highlighting the need for mechanistic, data-driven cardiovascular models that can interpret early-warning signal in terms of underlying system-level changes. This work presents a data-driven cardiovascular digital twin that integrates machine learning with one-dimensional haemodynamic modelling for continuous state estimation. ECG provides early-warning signal, while personalised haemodynamic modelling provides mechanistic interpretation. Inverse analysis and adaptive data assimilation within a closed-loop arterial network enable tracking of evolving cardiovascular states from routinely available physiological data. The methodology is demonstrated using sepsis as a clinically relevant use case characterised by rapid haemodynamic changes. A continuously adapting one-dimensional haemodynamic model satisfactorily replicates patient-specific arterial pressure waveforms over three successive 10-minute windows, with stable short-term forecasting under changing physiological conditions. Model adaptation enables consistent estimation of key cardiovascular quantities, including systolic, diastolic, and mean arterial pressure, as well as cardiac output, under sepsis-induced haemodynamic variability. Overall, this study presents a data-driven cardiovascular digital twin framework for modelling and monitoring cardiovascular dynamics, illustrated using sepsis as a representative use case. The work highlights how early-warning signals and mechanistic haemodynamic modelling can play complementary roles in future cardiovascular digital twin development.