Having researched their website...
It seems that although they call themselves a college, they advertise themselves as a "university". I surmise that they are aware of the difference between a name and an academic institution.
(Sivvus trolley collision in the fruit aisle led to a jam, Wed 14 Apr 2010, 22:31, 1 reply)

King's College London is a constituent college of the University of London.
However they retain their own degree awarding powers for students who prefer 'King's College London' on their degree certificates than 'University of London'.

It is I believe, in Britain at least, perfectly acceptable to state that you are going to college when you are receiving a university education. This is partly due to the fact that the term college (as referring to pre-university education) is only used to describe a few independent FE institutions, and also that many universities are comprised of constituent colleges such as in London, Oxford, Durham and Cambridge.
( TFD is sporting this season's finest necropants, Wed 14 Apr 2010, 23:25, closed)

Just looked it up... and yeah, I was wrong. :-)
So sorry, but speaking from my own experience of my own uni- the college is the house you belong to/place where you live/common room etc, whereas the university is the place where you study.
(Sivvus trolley collision in the fruit aisle led to a jam, Wed 14 Apr 2010, 23:37, closed)