Are Cambridge or Oxford universities ideal for working at NASA in futureWatch
Student life, in partnership with UEA
If you're aiming for that, then they're a reasonable place to start - I believe Cambridge has a pretty good Aerospace department. For NASA specifically however I would imagine a US university would make it easier to get a foot in the door - a quick Google tells me Massachusets, Stanford, Michigan - Ann Arbor and Texas A&M are all good.
If you'd prefer to study in the UK it may be worth looking into working with the European Space Agency. There's plenty of information out there, but for what it's worth I have a family member who studied at Leicester and now flies satellites for the ESA, and he raves about his time there.
Hope that helps a bit!
If your're international look at MIT, Georgia Tech, Stanford, Caltech, Berkeley etc. It will be much easier to get permission to work in the US if you study there.
Unless you have US citizenship or plan on getting it. it would be easier to work for the European Space Agency (ESA) instead.
What I've noticed, because I actually would love to end up working in the ESA, is that the people involved there have all sorts of different degrees from a wide range of unis. So it's what you do after uni that seems to matter more when it comes to this field.