Cine cardiac magnetic resonance (CMR) imaging is considered the gold standard for cardiac function evaluation. However, cine CMR acquisition is inherently slow and in recent decades considerable effort has been put into accelerating scan times without compromising image quality or the accuracy of derived results. In this article, we present a fully-automated, quality-controlled integrated framework for reconstruction, segmentation and downstream analysis of undersampled cine CMR data. The framework produces high quality reconstructions and segmentations, leading to undersampling factors that are optimised on a scan-by-scan basis. This results in reduced scan times and automated analysis, enabling robust and accurate estimation of functional biomarkers. To demonstrate the feasibility of the proposed approach, we perform simulations of radial k-space acquisitions using in-vivo cine CMR data from 270 subjects from the UK Biobank (with synthetic phase) and in-vivo cine CMR data from 16 healthy subjects (with real phase). The results demonstrate that the optimal undersampling factor varies for different subjects by approximately 1 to 2 seconds per slice. We show that our method can produce quality-controlled images in a mean scan time reduced from 12 to 4 seconds per slice, and that image quality is sufficient to allow clinically relevant parameters to be automatically estimated to lie within 5% mean absolute difference.