Constantły repeated by regime-controlled broadcasters, it became widespread. You'll notice in pre-war films the educated, middle-classers and cityslickers use the hard £ but the peasants they address often do the £=W thing. Except in eastern Poland where even hayseeds pronounce the traditional hard £.
An amusing theory, but not backed up by the facts which were that the communist media tried to keep up the kresowa pronunciation in formal contexts as long as it could and only gave up when not enough speakers could be found who could manage it.
The change of ł (or 'hard' l) in slavic languages into u, v, w or o sounds takes place across a number or Slavic languages either informally or formalized in the writing systems (note Serbo-Croation forms like bio for był) or Ukrainian бив (byw) for był.
The process is simply far more advanced in Polish than in the others where it's limited to certain positions.