Using "ringing" instead of "calling" is fine, and is a translation accepted by dictionaries. And secondly, using "who" would be much more natural here than "whom". Nobody I know would ever say "Whom are you calling/ringing/phoning?". From Oxford Dictionaries:
"In practice, most people never use whom like this in speech because it sounds extremely formal They don't use whom at all, and instead use who in all contexts, i.e.:
Who do you think we should support?
Who do you wish to speak to?"
Hi. I'm also British and an ageing RP speaker to boot, but I don't use "whom" very much in everyday language, especially not in a simple question like this. And evidence suggests that not many other educated speakers use it much either. This evidence comes from corpora, huge computerised collections of language usage, used by linguists, dictionary compilers and the writers of EFL (English as a foreign language) learning materials. As it's rather a subjective area I think I'll leave it to the experts (all sources are British). Note that when they say "informal", they mean normal, not colloquial.
This is from Practical English Usage, Michael Swan, OUP, a very influential book in the EFL world:
"Whom is not used much in informal English. We prefer to use who as an object, especially in questions.
Who did they arrest?
Who did you go with?
We use whom in a more formal style; and we must use whom after a preposition."
And here's Raymond Murphy, another very popular EFL author, writing in English Grammar in Use, CUP., talking about its use in defining relative clauses, eg "The man (who/whom/that) I love", where we generally leave out the pronoun anyway:
".. we do not often use whom. In spoken English we usually prefer who or that, or nothing"
You'll see much the same in dictionaries. I've already quoted and linked to Oxford a couple of comments back. This is what other British dictionaries have to say:
"In everyday spoken or written English, people usually use who rather than whom"
"We don’t use it (whom) very often and we use it more commonly in writing than in speaking" Cambridge
"Whom is only used in written English and in formal spoken English"
"whom ... often replaced by who, especially in less formal usage Chambers
I've written about the use of whom in some detail here:
I don't think that your sentence has anything to do with phone calls.
Edit: Ok, Jellei pointed out to me that this does in fact work. Added now. But note that this implies a context where you are not acquainted with the caller, so you would most definitely use the formal pronouns.
My sixpence worth-It is nominative case before and after "verbs to be" -am are art is was were wert be been and being" therefore is who . Back when I was in school in the 50's and 60's. However "is calling" I don't think is classed as a "verb to be " It drives me crazy when I hear people mixing up he and him etc especially in the papers and with newsreaders.