...but not in the way any sane member of the public would want. Ian Parker-Joseph, writing at the Libertarian Party blog, has a very interesting post about the bureaucracy setting up private companies (limited by guarantee) to perform work that you or I would expect to be state-run. The examples he gives are the Association of Chief Police Officers and SOLACE (Society of Local Authority Chief Executives and Senior Managers).
As Ian PJ points out, SOLACE advises on recruiting local authority chief executives and setting their salary levels. It includes several chief executives on its board, so there is a clear conflict of interest. As he says, it's a pretty clear case of racketeering.
One other interesting facet of this scandal which Ian doesn't pick up on is the fact that structuring these bodies outside the public sector makes them immune to Freedom of Information requests.
Handy, that.