Cambridge is a college based university, meaning that to be a member of the university, you must also belong to a particular college (of which there are about thirty). In 1852, however, legislation came into effect stating that students need no longer be members of a particular college in order to study for a degree, and Fitzwilliam House was founded in order to provide accomodation for such people (the name coming from The Fitzwilliam Museum which the house was built opposite).
In the mid twentieth century however, the college fee was introduced, whereby the government payed each college a fairly large annual fee per student studying there (today it's about £2,800). This meant there was no longer a need for Fitzwilliam House, and it refounded itself as a college in 1966 out on Huntington Road.

As a college, it's edging a bit on the remote side, although with the impending development of the West Cambridge Site it will probably find itself more popular. It's right next door to New Hall, which may have some advantages...

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