Greg has published on a range of topics in international law including on dispute settlement, sources of law, and, in particular, various aspects of trade law. His research principally examines the interaction between trade policy and public policy objectives such as improving public health, protecting the environment, and supporting sustainable development. 

He is co-founder and Co-Director of the Trade & Public Policy (TaPP) Network, the largest multidisciplinary group of academic experts on UK trade policy. Additionally, he sits as TaPP representative on the the UK's Trade & Sustainable Development Domestic Advisory Group: an independent body, tasked with monitoring and advising the UK goverment on issues relating to the implementation of the trade and sustainable development chapters of the UK’s trade agreements.

Greg is co-Director of the University of Bristol Law School Centre for International Law, and was also Co-Rapporteur for the International Law Association (ILA) Committee on Sustainable Development and the Green Economy in International Trade Law, which concluded its mandate in 2022. The ILA Lisbon Recommendations were adopted in June that year. 

As of 2023, he is joint-lead on an interdisciplinary three-year NIHR-funded project to examine the how governments can best present public health measures at the committees of the World Trade Organization.