Last month Britain told Russia its behaviour had to change before the relationship could change.
Russia denied any wrongdoing and in turn accuses the UK of aggression with deployments of troops to Estonia and Poland.
This report argues the two countries should find areas of common interest to work on together, despite the political stalemate.
One of the report's authors, Emily Ferris, said: "Russia is a very important partner for co-operating on things like organised crime and drug trafficking from Afghanistan through a lot of routes in Russia.
"International terrorism is something which affects all of us, and even cybersecurity."
They acknowledge the political difficulties facing London and Moscow in working together, but hope away from the public gaze, a gradual thaw in relations can begin to the benefit of both countries.