Food supply chains are receiving increased attention due to rapid depletion of natural resources, increasing quality standards and rising food safety and security concerns. Implementing sustainability practices in food supply chains is believed to overcome such emerging challenges. However, limited studies address sustainability implementation concerns, particularly in cold food supply chains. Thus, this study attempts to identify factors hindering sustainability implementation in cold food chain networks by considering a case of UK artisan cheese producers. Survey data is utilised to identify and prioritise barriers for implementing sustainability following fuzzy analytic hierarchy process and sensitivity analysis. The analysis identified several key barriers, including initial investment cost, firm size and unawareness of government regulations. The internal barriers significantly dominate the implementation of sustainability practices in comparison to external barriers. Lack of consensus regarding the concept of sustainability by different stakeholders is observed to be an issue negatively affecting the level of integration in SMEs. Findings will help food and dairy SME's in gaining competitive advantage through the successful implementation of sustainability practices.