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The emerging and existing light field displays are highly capable of realistic presentation of 3D scenes on auto-stereoscopic glasses-free platforms. The light field size is a major drawback while utilising 3D displays and streaming purposes. When a light field is of high dynamic range, the size increases drastically. In this paper, we propose a novel compression algorithm for a high dynamic range light field which yields a perceptually lossless compression. The algorithm exploits the inter and intra view correlations of the HDR light field by interpreting it to be a four-dimension volume. The HDR light field compression is based on a novel 4DDCT-UCS (4D-DCT Uniform Colour Space) algorithm. Additional encoding of 4DDCT-UCS acquired images by HEVC eliminates intra-frame, inter-frame and intrinsic redundancies in HDR light field data. Comparison with state-of-the-art coders like JPEG-XL and HDR video coding algorithm exhibits superior compression performance of the proposed scheme for real-world light fields.