Hi Grant,
310 FI was assigned on the 8th July 1957 to F. Lli Ringressi sdf of Via Monte Alle Croci 4, Firenze.
The style of your mark is that of post 1968. Some sources list the number in 1971, whilst others do not, so perhaps it around that time that the company may have disappeared. The registration number '310 FI' is now retired.
Thanks to your image, these details will soon appear in
Italian Silverware and Jewellery Manufacturers
Trev.