After Dave releases New Eden back in Arvine, good ol' Eden spreads throughout Dave's alternate timelines. This is what brings New Eden here.
They are briefly fought against when Dave and Mark team up during Part 1, in an attempt to stop them unleashing a global chemical attack on major oil, coal, quarrying etc. business owners, including Mark. They also planned on killing many major government members and royalty. Dave and Mark do manage to stop them, however, before Mark goes back against Dave and arrests him.
They feature much more during Part 2. After the character Serena Vasco is revealed, and the fact that she has been working to uncover lots of the crime running across the planet, she meets Kaelyn Shardfast. There it is revealed that the New Eden Movement had in fact infiltrated the crime ring Dave worked for in Part 1, and were running various hits on establishments around London. The whole story tells of how Kaelyn and Serena work to fight against them, without alerting James and Ian to their alliance.