And will it possible to use the Schengen visa to visit Italy etc?
Short answer: Yes.
I have several friends from South Africa who have either moved to the UK, or who have been just visiting the UK.
They regularly then apply for Schengen visas - multiple entry, especially if they're doing a big trip - like one that includes darting off to Egypt or similar. A multi-entry Schengen visa certainly exists, and you can certainly apply for it from the UK, even if not a British Citizen.
Finally, I believe you specify on the application where you want to go, so mentioning Italy would make that easy, but regardless, you can travel anywhere within the Schengen area once you're inside - there are no borders.