I am in same situation and took legal advise on this. Brace yourself for bad news! The CSA can only help if there is UK income although UK residency is not needed. If there is UK income they can trace through inland revenue and make direct deductions. If no UK income then you can get a court order for anxillary relief and then seek to get it enforced through foreign courts (Not sure if Italy is signatory to the treaty but I expect so as in EU. My ex is in USA). However obviously costs and times of this is likely to be more than you will ever get back...
Unfortunately, unless the CSA have been involved and she received maintenance whilst he was in the UK, it falls outside of what they will get involved with to chase up an absent parent in another country.
There is a list of countries UK has agreements with, but it needs that CSA connection prior to them going abroad.
In the same boat here to a degree, but my XP does pay voluntarily (UK citizen, residing the other side of the world!). If he stops paying, I've no way of any legal enforcement action.
It's a warning to all really - involve the CSA just in case they move abroad!