Almost all major universities are “public” in the sense that they are funded partly by the government and are regulated by the Office for Students (OfS).
A UK “private” university must be officially recognized by the UK government to award degrees. If it’s recognized, the degree holds the same legal status as one from a public university.
Recognition of the universities is associated with the OfS Register and having degree-awarding powers, not the funding model.
Employers and immigration authorities care about whether the university is recognised and reputable, not whether it’s public or private.
A degree from a well-ranked UK private institution (e.g., University of Buckingham) can be as valid as one from a public university like UCL — but employers may simply be more familiar with the big public names.
