Upvote:3
Assuming that you are currently inside the Common Travel Area, your question is based solely on whether or not you get randomly picked for a challenge. It's not very often that happens.
In the case that it does happen, your Italian passport will work as proof as long as the photo reasonably looks like you and your personal details dovetail with your other forms of ID such as driving permit, birth certificate or whatever else you can offer.
It's reasonable to expect that they are not going to be altogether happy about your travelling on an expired passport so you should pad in some extra time for them to land you in the UK.