In recent years, responsible sourcing and procurement (including green supply chain management) across the architecture, engineering, and construction (AEC) sectors have become notable contributors to sustainable construction strategies. This study aims to provide a systematic review of responsible sourcing literature across the AEC sectors of the UK to identify a suite of opportunities and obstacles to adopting ethical and environmentally supportive practices and to highlight avenues for further investigation. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) review process was adopted to identify, screen, and select (n = 80) articles (from 2000–2020) for review. Analysis of these articles identified the most frequently reported opportunities: (i) stakeholder value (40%); (ii) improved supply chain performance (39%); and (iii) competitive advantage (30%). The most frequently reported obstacles relating to the uptake of responsible sourcing are the following: (i) cost (44%); (ii) industry constraints (28%); and (iii) lack of frameworks/information and lack of awareness (25%). Given the industry importance of these themes, it is proposed that there is a necessity to explore and unravel the perceptions of industry experts about these issues so as to clarify the progress and possibilities for more widely adopting responsible sourcing across the AEC sector and, moreover, for clarifying their contribution towards achieving national and international sustainability targets (e.g., UN Sustainable Development Goals).