Love it, love it, love it.
If you are thinking of a site, make a site of the home of Cambridge University, Cambridge.
Since the UK does not use .edu (.ac.uk) there is no issue there. Also, it appears it is more proper to refer to this majestic place as the University of Cambridge.
I think a site focusing on the features of the village of Cambridge followed by a virtual tour of the University. If your focus is different, I think there will be no issues. But, I am not an attorney and I do not guarantee success.
Even when it is not my name, I still get excited for other people when I see the potential in a name.That is good advise you clever genius you!
They are all Direct type-ins... possibly by future students, simply typing in the domain into the address bar.
*the exceptional businesses of our esteemed moderators