Other Italian immigrants just did not want to loose their own nationality and preferred to stay as they were, some intended to stay a short time and make some money to take back home, others were and are proud of their origin and wish to remain Italian even though they settled down within the UK.
Did you know ………….
Women who had British nationality were automatically considered Italian in the eyes of the British Government when they married an Italian. Therefore they were also called “Aliens” when WW II broke out and had to request and sign for re admission when the war was over, many of these can be found in the London Gazette.
If your Grandfather or Great grandfather did not become British and did not serve with the British army, then you and your family are entitled to Italian nationality.