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The polarisation of light induced by aligned interstellar dust serves as a significant tool in investigating cosmic magnetic fields and dust properties, while posing a challenge in characterising the polarisation of the cosmic microwave background and other sources. To establish dust polarisation as a reliable tool, the physics of the grain alignment process must be studied thoroughly. The magnetically enhanced radiative torque (MRAT) alignment is the only mechanism that can induce highly efficient alignment of grains with magnetic fields required by polarisation observations of the diffuse interstellar medium. Here, we aim to test the MRAT mechanism in starless cores using the multi-wavelength polarisation from optical to submillimetre. Our numerical modelling of dust polarisation using the MRAT theory demonstrates that the alignment efficiency of starlight polarisation (p_ext/A_V) and the degree of thermal dust polarisation (p_em) first decrease slowly with increasing visual extinction (A_V) and then fall steeply as ∝A_v^-1at largeA_Vdue to the loss of grain alignment, which explains the phenomenon known as polarisation holes. Visual extinction at the transition from shallow to steep slope (A_V^loss) increases with maximum grain size. By applying physical profiles suitable for a starless core, 109 in the Pipe nebula (Pipe-109), our model successfully reproduces the existing observations of starlight polarisation in the R band (0.65 μm) and the H band (1.65 μm), as well as emission polarisation in the submillimetre (870 μm). Successful modelling of observational data requires perfect alignment of large grains, which serves as evidence for the MRAT mechanism, and an increased maximum grain size with higher elongation at higherA_V. The latter reveals the first evidence for a new model of anisotropic grain growth induced by magnetic grain alignment. This paper introduces the framework for probing the fundamental physics of grain alignment and dust evolution using multi-wavelength dust polarisation (GRADE-POL), and it is the first of our GRADE-POL series.