The existing body of knowledge on the Modern Methods of Construction (MMC) reflects their benefits and relative advantages, particularly in addressing contemporary construction challenges. However, the uptake of such methods is minimal, particularly in the public construction sector. The low uptake has led MMC firms to liquidation due to the lack of an economy of scale. Studies, particularly recently, explain that the low adoption rates are linked to the inappropriateness of existing business models responsible for driving broader demand. This paper assumes that the lag in MMC adoption could be related to the ability of supply business models to communicate confidence to demand. Public clients are foreseen as important target customers, acquiring influential status across the industry, with an expected potential to drive innovation adoption across the sector. A systematic review method allows scholars to assess existing literature by critically locating and analysing relative publications to approach the study’s aim. Through utilising this method, the study classifies the arguments against the Business Model Canvas (BMC), and argues the results with respect to contingency theory, and in turn, synthesizing a new meaning that reveals the considerations needed to boost business model performance when penetrating the public sector. Hence, the critical analyses of 70 studies relative to MMC, led to proposing the contingencies that are believed to better structure business models. Results suggest that MMC firms can embrace specific reforms and gain more momentum when communicating confidence to public client organisations; however, a guideline that conceptualises the interactions between the elements and their influence on the decision-making does not exist, and this may be inhibiting coherency on how MMC businesses drive broader demand. To the authors’ knowledge, this is the first study to utilise the contingency theory as an attempt to disseminate previous efforts to explain the low adoption of MMC in the UK public sector.