Thank you so much Maddy, this is what I have discovered doing my own research in Pembrokeshire. There was an area behind Pembroke Castle called 'Catshole Quarry', which goes back centuries as a place where gypsies would live. The BBC and newspaper did an article on gypsies in Pembrokeshire, and they found this area was originally outside Pembroke Town walls, and 20% of the local population were found to have gypsy roots. This part of history seems to have been written out. However in the 19th century it seems to be settled in the rough end of Pembroke town, they weren't only Italian but they were also Irish and some English. They're newspaper cuttings about the Price family living at the quarry having disputes.
The presumption that the shops were chandlers or anything to do with boats and ships are mistaken. As fellow Rootschats have discovered. It is a shame that some of the historian's archives in Pembrokeshire they refer to the shops being to do with boats and ships. I think one reason is because they were very near Ropewalk Terrace, a very popular name in ports around the country. Originally it was plain ropewalk and because Pembroke is built on a long rectangular stone mound, the only place to make rope was outside the town walls in a field called Rope Walk.
So the family tradition was as described via your link, and they were as surprised as I was to discover the true meaning of the shops. My family certainly looked Italian very dark skinned, but I have a photo of one of the original Italians, and he does look very much non-European. It's early days so I don't know if he was genetically Roma, gypsy, or traveller, it's all a bit vague in my head.
But thanks for the link very interesting. Steven