Dear Esspee, no it is both correct and more polite to say May I have rather than can I have.
If you say may I, you are asking permission, if you say can I do something, you are strictly speaking asking whether you are capable of doing it.
As Professor Dumbledore said to Harry Potter in the first book (and film) where Harry asks "Can I ask you a question, sir?" "Obviously, you have just done so; you may ask me a question"
All through my childhood, my father made similar remarks to any child unwise enough to use can instead of may.
"Can I get down from the table?" was invariably answered with "I imagine you are physically capable of doing so, but if you are requesting my permission, you mean "May I please leave the table?"
Anyone else out there remember such remarks?