The original of at least part of it
Let Zygons be Zygons

According to the film credits, Sylvia Fine (Kaye's wife) wrote the music and lyrics for the Opera Number.
Yes but she is also credited for "The Little Fiddle" as well, which i definitly taken from well know classical music.

Whatever it is it most definitly was not written for the film because I have heard sections of it in other things. Sylvia Fine's credit is for aditional lyrics. For instance the aria from it is used in an opera scetch in 'The Two Ronnies', and the same piece is used intrumentaly in some Carry On films.

According to the film credits, Sylvia Fine (Kaye's wife) wrote the music and lyrics for the Opera Number.

Definitely not written for the film. The following is from The Two Ronnies. Stating from 32:30 is an opera sketch which uses some of the same music.
Let Zygons be Zygons

It's a pastiche of several operas, primarily, yes, Il Trovatorethe "Miserere" scene at the end of that opera, but mostly it's just musical cliches found in lots of operas. The "Si Puo" that he starts in with is from I Pagliacci. I would hazard a guess that Sylvia Fine is quoting at least a dozen in fragments. I do notice that one of the voices used to dub the female singer is Miliza Korjus, very distinctly, but only on the highest notes. Highly recommend her! Wonderful singer, forgotten today.

In the theatre I noticed a poster for 'Cavalleria Rusticana' - but I don't know if that was the actual opera being performed! I think it was written for the movie.
I thought Danny was hilarious posing as an opera singer!

I think the opera number was written for the movie and not taken from another work. I could be wrong.
"A child of five would understand this. Send someone to fetch a child of five."