HEPI have published a study on private providers in the UK by Fielden and Middlehurst - two commentators who know their stuff http://www.hepi.ac.uk/455-1969/Private-Providers-in-UK-Higher-Education--Some-Policy-Options.html. There are a lot of valuable things about this report.
Fielden and Middlehurst very properly underline the role of not-for-profit private providers both in the US and UK, and avoid the whiff of moral panic that sometimes attends the discourse about for-profits. They lay out reasonably clearly the regulatory 'structure' for private providers in the UK. But I can't help feel the issue they avoid - student number control - is the key issue. I'll blog more on this later.