The unit, to be organised by the Foreign Policy Centre, a think-tank whose president is Robin Cook and whose patron is Mr Blair, has been proposed as part of the attempt to prove that Britain is still committed to Europe - despite the decision to delay entry to the single currency.
Joint papers and policy recommendations on areas such as welfare reform, crime and unemployment will be published following seminars. Advisers will be seconded to London from Europe, and staff from Downing St and the Foreign Office sent abroad to discuss "Third Way" ideas.
The move will further infuriate Eurosceptics, already angry about the co-operation on policy through working groups, like the Anglo-German one involving Peter Mandelson and Bodo Hombach which met on Friday. They believe collaboration will increase the likelihood of a European federal superstate.
Mark Leonard, head of the Foreign Policy Centre, said: "The debate about the Third Way is ... part of a debate about social democracy going on across Europe. We need to have a single debate rather than 15 separate national debates."