There is , as you say, significantly higher private investment in the SE than in the regions. However, much of this goes on projects to which the public sector contributes. There is a need for this investment model to be encouraged regionally.
Hang on, public spending is the only thing that keeps some parts of the country going, given that there are towns which are dying and the world left behind. I grew up in one of them, all the public money in the world in the hands of "local government" just was ****ed up the wall. Are you asking for more public subsidy for places which have fallen so far behind that no business can see a return on investment?