Radiomics is an emerging technique for the quantification of imaging data that has recently shown great promise for deeper phenotyping of cardiovascular disease. Thus far, the technique has been mostly applied in single-centre studies. However, one of the main difficulties in multi-centre imaging studies is the inherent variability of image characteristics due to centre differences. In this paper, a comprehensive analysis of radiomics variability under several image-and feature-based normalisation techniques was conducted using a multi-centre cardiovascular magnetic resonance dataset. 218 subjects divided into healthy (n=112) and hypertrophic cardiomyopathy (n=106, HCM) groups from five different centres were considered. First and second order texture radiomic features were extracted from three regions of interest, namely the left and right ventricular cavities and the left ventricular myocardium. Two methods were used to assess features’ variability. First, feature distributions were compared across centres to obtain a distribution similarity index. Second, two classification tasks were proposed to assess: 1) the amount of centre-related information encoded in normalised features (centre identification) and 2) the generalisation ability for a classification model when trained on these features (healthy versus HCM classification). The results showed that the feature-based harmonisation technique ComBat is able to remove the variability introduced by centre information from radiomic features, at the expense of degrading classification performance. Piecewise linear histogram matching normalisation gave features with greater generalisation ability for classification (0.75 ± 0.09). Models trained with features from images without normalisation showed the worst performance overall (0.47 ± 0.13). In conclusion, centre-related information removal did not imply good generalisation ability for classification.