Bonjour
ATIS is only required for boats more than 20m. Otherwise any hand held VHF is sufficient and only required on some specific area (Paris for example).
The issue of keeping the British flag for the journey to Italy is mainly an insurance issue.
For example, I found a French insurance, but it was not obvious, that covered my Dannish boat for the travel from Copenhagen to Britanny.
I suppose that the boat is actually registered in the "small boat registration" category.
You must have a paper provided by the seller indicating that the boat has been cancelled from the registration.
Formelly, your boat should be registered to travel out of the national country watters and I'm not sure that the "small boat registration" is valid for international travels (BREXIT).
For example :the Dannish boats are not registered under 20m and I travelled all around Europe without any problem; but it was not formally correct. In case of problem, my English would have been very poor and I would have play the fool (Latin way of life).
If you by the boat from a physical person the VAT will be supposed to be already paid.
Eric