I'm not denying that News Corporation is influential, I just think the primary motivation is profit rather than an actual desire to see through any kind of political agenda.
Tony Blair is the godparent of one of Mirdoch's children. Those two deserve each other with their insidious and seedy behavior. Profit may be a motivation for them both, however Murdoch is far more clever and manipulative than Blair and his agenda would hardly be hurt by having the PM as a godparent to his kid.
In the UK/Australia, News Limited has been heavily involved through its newspapers in dictating government policy. For example the "boat people" issue was very much promoted in Australia and in the UK there are countless examples of governments capitulating on policy at the behest of the News International papers.