Multiple kernel clustering (MKC) optimally utilizes a group of pre-specified base kernels to improve clustering performance. Among existing MKC algorithms, the recently proposed late fusion MKC methods demonstrate promising clustering performance in various applications and enjoy considerable computational acceleration. However, we observe that the kernel partition learning and late fusion processes are separated from each other in the existing mechanism, which may lead to suboptimal solutions and adversely affect the clustering performance. In this article, we propose a novel late fusion multiple kernel clustering with proxy graph refinement (LFMKC-PGR) framework to address these issues. First, we theoretically revisit the connection between late fusion kernel base partition and traditional spectral embedding. Based on this observation, we construct a proxy self-expressive graph from kernel base partitions. The proxy graph in return refines the individual kernel partitions and also captures partition relations in graph structure rather than simple linear transformation. We also provide theoretical connections and considerations between the proposed framework and the multiple kernel subspace clustering. An alternate algorithm with proved convergence is then developed to solve the resultant optimization problem. After that, extensive experiments are conducted on 12 multi-kernel benchmark datasets, and the results demonstrate the effectiveness of our proposed algorithm. The code of the proposed algorithm is publicly available at https://github.com/wangsiwei2010/graphlatefusion_MKC.