Will it cost me to use internet in Italy for the next 4 days

MSF , is correct that you will have 12GB of data to use for free, but if you do need access to your full plan, you can buy EU Data Passes an add-on. Here is a link with more details https://bit.ly/3kExGXy 

If you have a current smarty plan, then you can use it in Italy (as this is an EU country).

You can use it as you would at home BUT you can only use a max of 12Gb data while roaming, no matter if your plan allows more while in the UK.