"May I" Vs "Can I" - just out of curiousity

Pardon if this is not the correct location for this discussion, I’ve only been a member a couple of days.

I have a friend from Spain that recently went to a school in England to learn English. (I just came from a trip to Europe). I met many ESL students there trying to learn English and they would always try to spend time with me to practice rather than with the Brittish people around them because as they insisted that my North-East American accent was much easier for them to understand than British English. During our travels, one person mentioned that they were taught that “may I” is formal and used with strangers or superiors while “can I” is informal and used with friends and such. In grade school I was taught that “can I” is incorrect when asking for permission because can = able. That when asking for permission the correct usage is “may I”. In American society it is true that “can I” is used more often, but technically speaking is it correct? I’m trying to see if what I learned in grade-school has any merit.

I learned what you learned, if you ask for permission, you should use “may I”. I’ve actually asked my parents something saying “can you [do something for me]?” They would say “Yes, I can”, then do nothing, because I said “can I” instead of “may I”.

In practice, I always say “can I” or “would you mind if I”. “May I” sounds stilted to me for some reason.

It’s the same in British English. “May I” is technically correct when asking for permission, but isn’t that often used in everyday conversation. It does sound quite formal and for this reason it’s used in some rhetorical questions, which aren’t looking for an answer, but used to add a somewhat demeaning, condescending or pompous effect. For example:

“May I say, I think the service here is an absolute disgrace.”
“May I just interrupt you on that point…”
“May I please ask that you give me a little respect here.”

…where the “may I” is usually emphasised to add a little extra weight to the condescending manner.

Having said that, ordinary uses of “may I” (with real questions as opposed to rhetorical ones) always sound polite, and correct:

“May I ask for the bill please?”.
“May I see those photographs you took last weekend?”

It seems then that when they teach English to ESL students they now teach that “may I” and “can I” are both correct in asking for permission, but that “may I” is simply the formal tense. I suppose if you take into account the regular day to day usage of the terms, they are teaching them correctly. For instance, even though I know “may I” is correct when asking for permission I also know that if I were to use it people would maybe laugh or think I’m being pretentious. I only use it in business/professional situations. But does this mean that on actual written exams for non-english speakers “can I” & “may I” are now both considered correct?

May I say that “may I” is still the correct way of saying it but that many, many people these days say “can I” instead? I generally use “may I”, but can I add here that my daughter uses “can I” most of the time?

The whole “can I” thing reminds me when I was in grade school and when I askedd “can I use the restoom?” My teacher chuckled and said," I don’t know, can you?" She then went on to correct and told me to use “may I.”

Since I still typically use “can I” around my family, I do think teaching “may I” as formal and “Can I” as informal makes sense.

I would never use “can I” instead of “may I” in formal written English, probably even in emails etc. to friends/family. But then I’m a bit of a stickler for these things !

So the vote is in. I asked because I might want to start tutoring English here eventually (after I get the hang of LingQ)… and I imagine that some people learning English will be practicing for formal test requirements. What the ESL students told me they learned made me wonder if when tutoring it would be responsible to teach that “may I” is correct and “can I” incorrect when asking for permission.- Just as I learned myself growing up.