You need a rapid test 48 hours before and must quarantine for 5 days, after which, you must take another Covid test, and ,if negative, you are free to roam around.
https://www.salute.gov.it/portale/nuovocoronavirus/dettaglioContenutiNuovoCoronavirus.jsp?lingua=italiano&id=5411&area=nuovoCoronavirus&menu=vuoto
Change your flight to avoid the UK, and your CDC card will suffice. Actually I suggest to avoid layovers in third countries at this time, that way you deal with the regulations of only two countries (Italy and USA). I presume you are flying American. Change your flight and have a layover at JFK or PHL, instead of LHR. American Airlines flies to FCO, MXP, VCE, BLQ, at least on normal times, not sure if now they fly only to FCO.