Thank you to 13901 for his assistance so far.

Has anyone got experience of trying to book a Rapid Antigen test online at the facility in T1 at MXP run by Gruppo San Donato? It seems virtually impossible for a non-resident given the website is only in Italian, you have to register first before booking and as part of this registration it asks for an Italian Tax Code (Codici Fiscale). A temporary ((fake?) Codici Fiscale can be generated on-line but then the payment portal just seems to hang up each time.

3 weeks ago they accepted an e-mail booking but this time after 3 sent e-mails they just do not reply.

So does anyone have any experience of just turning up at MXP and having a test done....I really can't imagine many non-Italian folk having managed to book this online?