Use of bioenergy as a renewable resource is increasing in many parts of the world and can generate significant environmental, economic and social benefits if managed with due regard to sustainability constraints. This work reviews the environmental, social and economic constraints on key feedstocks for UK heat, power and transport fuel. Key sustainability constraints include greenhouse gas savings achieved for different fuels, land availability, air quality impacts and facility siting. Applying those constraints, we estimate that existing technologies would facilitate a sustainability constrained level of medium-term bioenergy/biofuel supply to the UK of 4.9% of total energy demand, broken down into 4.3% of heat demands, 4.3% of electricity, and 5.8% of transport fuel. This suggests that attempts to increase the supply above these levels could have counterproductive sustainability impacts in the absence of compensating technology developments or identification of additional resources. The barriers that currently prevent this level of supply being achieved have been analysed and classified. This suggests that the biggest policy impacts would be in stimulating the market for heat demand in rural areas, supporting feedstock prices in a manner that incentivised efficient use/maximum greenhouse gas savings and targeting investment capital that improves yield and reduces land-take.