Previously we demonstrated a combined scanning-point optical coherence tomography (OCT) and Scheimpflug Imaging (SI) system, to provide cross-section images of the corneal layers and the whole anterior segment of the eye simultaneously. However, to fully realise the benefits of this dual imaging modality concept towards clinical practice, it is required that the OCT part of the system can achieve ultra-high axial resolution (<3 µm in air) and faster imaging speeds, without using prohibitively expensive components. To achieve this, a new imaging device integrating line-field OCT and SI, using a supercontinuum light source, is demonstrated. This line-field configuration enables both OCT and SI B-scan to be captured using the same light illumination in a single shot, which is the most significant improvement over single point scanning. This achieves an OCT axial resolution down to 2.1 µm in air (1.6 µm in corneal tissue) and an imaging speed up to 213 kA-Scans/s. Since the OCT and SI capture the identical corneal position and serve as cross-validation, this technique offers a great method for accurately determining the individual corneal thickness and refractive index, thereby minimizing individual variations, which can help determine the extent of cutting or correction needed in vision correction. Moreover, the precise measurement of corneal thickness provided by this technique allows for a better understanding of the biomechanical properties of the cornea. We demonstrate the efficacy of the proposed system by evaluating porcine and bovine eyes ex-vivo for determining the corneal refractive index and thickness.