Mixed Blocking Permutation Flowshop Scheduling Problem (MBPFSP) with the objective of makespan minimisation is NP-Hard. It has important industrial applications that include the cider production industry. MBPFSP has made some progress in recent years. However, within practical time limits, existing incomplete algorithms still either find low quality solutions or struggle with large problems. One key reason behind this is the typical way of using generic heuristics or metaheuristics that usually lack problem specific structural knowledge. In MBPFSP, a machine could be blocked with the currently finished job until the subsequent machine is available to process the same job. These blocking constraints affect the makespan. So MBPFSP search should naturally take explicit steps to take the blocking constraints into account. Unfortunately, existing research on MBPFSP just uses only the makespan to compare generated solutions, but the search otherwise is not aware of the blocking constraints. Moreover, existing such methods use either an exhaustive or a random neighbourhood generation strategy. In this work, we aim to advance MBPFSP search by better exploiting the problem specific structural knowledge. We use the constraint and the objective functions to obtain such problem specific knowledge and we exploit such knowledge both in a constructive search method and in a local search method. In this paper, we also present an acceleration method to efficiently evaluate insertion-based neighbourhoods of MBPFSP. Our experimental results on three standard testbeds demonstrate that our proposed algorithms significantly improve over existing best-performing algorithms.