I have a house in Italy but am here for less than half a year, have no Italian income and am not tax resident. I need to transfer money into my Italian bank account to pay for house improvements. Is there a way of getting a bit of interest while the money is sitting there without getting drawn into the Italian tax system? For example an account that deducts tax at source?

Have you looked at Wise Interest? They pay 3.5% on GBP. No need to enter into the Italian tax system.
https://wise.com/gb/interest/

You can put it into a Wise account and get cash back that’s taxed at source at 30% - they’re based in Belgium. You can instead opt in for their interest option but it’s subject to Capital Gains.