I was asked this question in a comment - I guess it would be a good idea to explain more clearly what an Erasmus Exchange is!
For me anyway;
Erasmus is something you MAY choose to do as part of your studies - you have to be a university level student and have completed your first year of study I think.
You choose a country and an institution you want to study at and need to make an application to go there. For example, I knew specifically I wanted to study in Norway as it would really benefit future plans (particularly with the language) so I looked at applying to both Oslo and Bergen.
You need to check with your own university what their specific process is - some have very rigid paperwork you have to follow - mine kind of left the whole thing up to me to sort out! I think though, its your responsibility to research the institution you like and check that they have relevant courses that fit in with your degree - then you can apply - I had to send a portfolio and a letter of motivation.
Basically if you are doing a degree and want to do an exchange there is nothing really stopping you - it is encouraged I think but for some reason it doesn't seem to be as popular in England as in other European countries - some courses actually require it too I think.
You still get your usual student loan and an erasmus grant (unlike a loan so you don't pay it back) although saying that - today is EXACTLY half way through my exchange and I still haven't had it :S If you study for 1 semester you pay for your course at home still - if you study abroad for a year you wont pay any course fees for that year. You DONT pay fees at the institution you study at abroad as far as I know.
Finally, the exchange is normally recognised as part of your degree, and even if it is not you will get a special 'mention'. Again something you check with your uni :)
I have included a couple of links for anyone wanting to look further, but my suggestion would be having a word with your university first anyway.