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You often hear that almost all UK universities are public. Wikipedia, for example, says "There are four fully-fledged private universities in the United Kingdom, the University of Buckingham, BPP University, Regent's University London and the University of Law."
However my understanding is that funding for UK universities comes almost entirely from tuition fees and grant income.
What is the legal/technical/practical difference between a public and private university in the UK?
However my understanding is that funding for UK universities comes almost entirely from tuition fees and grant income.
This is incorrect. Tuition of UK students is subsidised (to varying amounts in the constituent countries of the UK). In the most extreme case, Scottish students pay no tuition at universities in Scotland. If you compare 'home' fees with international fees at any public university, you will see that UK and EU students pay substantially less than international students (although it is not the case that the UK government tops up the UK tuition fees to the amount paid by an international student).
Sheffield University has some informative pages on how exactly this funding works. In particular, student tuition is subsidised via HEFCE grants, which vary depending on the course. This page appears to date from before the new variable fee regime in England, so the numbers and formulae may be out of date. But the funding mechanism subsidises the clinical years of medical, dental and veterinary students the most, then lab based courses and the non-clinical years of the medical courses, then courses with some lab or fieldwork, and then everything else.
Private universities do not receive this funding.
In England the government provides ~£4 billion to fund universities via HEFE. About 1/3 of this is for teaching, 1/3 for research and a bit less for captial spending and other costs. There are different bodies for Scotland and Wales but I suspect they work similarly.
There is lots of info on the HEFE website about how the funding is allocated etc. I haven't looked too deeply, but the teaching funding is split almost evenly between supporting high cost subjects (e.g. physics/engineering) and supporting low access groups.
This funding is a small but significant % of university funding ~15% according to wikipedia.
In return the universities have to follow various regulations. The most significant of which is the tuition fee cap (~£9,000 currently) and do various things encourage encourage disadvantage groups to go to university.
Theoretically any university could refuse this funding and become private. However, I will speculate that the increase in tuition fees required to cover the loss would make them unattractive to students compared to public universities.
