There is more than one category of "non-magical" people. There are Muggles, Squibs and Witches/Wizards who have lost their magical powers because of some traumatic incident.
I do not think that JKR would mislead us in terms of Petunia and Dudders. Uncle vernon seems, on the face of it, an unlikely candidate although some of the views of his sister Marge are very similar to to the worst of Voldemort
's followers, "bad blood" etc.
My immediate guess is Mrs. Figg
for the simple reason that she has had continued and significant contact with the magical community, that she has had had a continued role in the protection of Harry
, that she appears to have accepted that she is a squib, in contrast to Filch who has tried to overcome this problem.
When I think about Madam Pomfrey I cannot remember any magic that she has performed. She has used potions and unctions created by other Witches/Wizards but nothing specifically magical instigated by herself. Dumbledore
always preferred to be taken to Snape
The other significant figure that I have just thought of, and I now take back what I said about Mrs. Figg
, is that old fraud Sibill Trelawney, who, as far as I recollect, has never performed any magic in her life.