The adhesion capabilities of sulfuric acid and tartaric-sulfuric-acid anodic oxide films on cladded AA2024-T3 aluminium substrates have been investigated in a quantitative manner. A relatively simple, versatile and industrially applicable test methodology based on DIN EN ISO 29862 has been used. In addition, the effect of anodising process parameters on the oxide film morphology has been studied and correlated with the adhesion results. The process parameters considered are the chemistry of the acidic pickling pre-treatment step, the addition of tartaric acid to the sulfuric acid electrolyte, the formation voltage, and the electrolyte temperature. The suggested tape peel adhesion test is able to differentiate among pre-treatments and anodising conditions showing a good correlation with the morphological features at the ultimate surface. High peel adhesion strengths are measured when topographies such as pore mouth widening and dissolution-driven roughness take place. These morphologies are typically found in anodic layers formed at elevated electrolyte temperatures. The proposed method can be beneficial for a fast assessment of anodising parameters for good adhesion, which is of special interest for the industrial optimisation of anodising processes.