Hybrid MRI linear accelerators (MR-linacs) enable real-time image guidance during radiotherapy. Under real-time MRI, a compromise must be found between spatio-temporal resolution and SNR, whereas to precisely track tumour position, both should be maximised. The presented method implements a motion-adaptive image reconstruction based on a golden-angle radial acquisition scheme. This allows producing SNR-optimised images under periods of small motion and images optimised for temporal resolution when motion is larger. The technique was implemented at a low-field MR-linac (0.35T) to image a free-breathing volunteer and a motion phantom.