No, that's a simplification. In the strict sense, only Bliar, Brown and Schröder are third-wayists. However, they inspired Prodi (who, lest you forget, failed to curb media monopolies, but executed a lot of 'reforms' in the name of budgetary discipline for the introduction of the Euro -- even if the end result was still much more welfare state than in Britain), Sócrates, Almunia, Zapatero (at least initially when he even praised Bliar, and arguably all the way until he dumped Almunia), and a couple of others (especially in the new EU member states) who never declared themselves Third Wayist, or even claimed they aren't, based on some differences. And the Third Wayists were also the logical continuation, with only minor steps forward, of the 'reform'-ism/defeatism in the face of neoliberalism signified by leaders like Göran Persson, Poul Nyrup Rasmussen, Wim Kok, Massimo D'Alema, and Felipe González. Jospin was the left-most of the whole bunch of Socialists dominating the EU at the end of the nineties -- and the successors in opposition seem to have made up for the distance. So the problem is really wide, deep and long-running.

_{*Lunatic*, n.
One whose delusions are out of fashion.}