well in order to be able to work, I resorted to the ultimate solution - full reinstall i.e. deleted TextMate.app and all the local files from ~/Library/Preferences/com.macromates.textmate* and ~Library/Application\ Support/TextMate/
After a new install everything works fine as before... It is really weird as I still do not know what happened as I surely didn't play with these files before as it worked out of the box for me...