I find it very interesting that Edith Annie said her father was Henry Veitch, Gamekeeper. It was not uncommon for illegitimate children to adapt the details of a stepfather (or sometimes a grandfather etc).
The Elizabeth Veitch who married in Morpeth in 1876, as per my earlier post, married Henry Storey, who was a gamekeeper at the time of the 1891 census. Not concrete evidence, but v interesting.
I did consider whether Edith might have been placed with Margaret Purdy as a nurse child by the poor law authorities, particularly as Edith is described as a boarder in 1881. However, Edith would have been the responsibility of Morpeth, not Gateshead, where Margaret was living by then.
You can confirm the name of Margaret's father by getting her marriage cert, unless perhaps Trich already has this as part of her Purdy research. I would keep digging for a relationship connection, quite possibly along the female line.