Although EU imports of illegal timber have halved since a previous Chatham House report on the subject in 2010, Mr Davies said more could be done.
He said: "While it is encouraging that illegal timber imports to the UK have halved, it is vital that we remove the market for illegally logged timber in the UK altogether. One way is to ensure we have a sustainable forestry and wood-processing sector that can supply more of our timber needs. Government can aid this by enabling the sector to plant more trees now and in the future."
The APPG on Forestry is supported by Confor. In addition to tackling illegal logging, Confor estimates that more investment in the UK forestry sector could deliver an additional 7000 jobs in deprived rural areas, while increased planting could mean that by 2050, forestry alone could reduce the UK's annual greenhouse gases emissions by 10 per cent.
Stuart Goodall, chief executive of Confor, added: "The need for increased levels of sustainable forestry and support for the wider forestry and wood processing sector has never been more important. The sector needs a secure long-term supply of timber, and woodlands need to be managed responsibly to protect them from climate change and pests/diseases."