I have found a birth record that I believe may be that of your great-grandmother Annie.
I was intrigued by the information you provided and I wondered what happened to Eddie’s mother, Sabina Scamp, as I could not find a death record for her.
In my experience of researching my own traveller ancestors, I found they sometimes had a tendency to use different names, so I began to wonder if Sabina Scamp and Elizabeth Lee were actually the same person.
With this in mind, I searched Kent birth records of the period using the surname Scamp and found:
Mary Ann Scamp born 26th July 1908 in Blean, Kent. The mother is Sabina Scamp, a hawker. No father is listed but this is not surprising as her parents were not legally married at the time of her birth (also very common amongst travellers of the period). I believe this also points to Annie and Eddie being full siblings, not step siblings.
I have tried to attach the pdf for you to view. I hope this helps.