Is it appropriate to ask a Professor to write a recommendation letter for applying to another university? I am currently studying at an university in Europe (undergraduate, first year)and would like to transfer (next year or in two years) to an university in UK. UCAS requires a reference to accompany your application.

I have a very successful academic career, I have taken all exams of my year and also some of my next years, and have obtained the highest mark ("cum laude") in almost all of them. The reason for transferring, therefore, is to get into a more challenging university.

Is it appropriate to ask a professor of my current university for a reference letter, given that it will be used as part of an application to another university?
Yes!

In fact, it would be inappropriate not to ask at least one professor at your current university for a reference letter, as direct evidence of your success.