Why dont you apply for a "special guardianship order". It is practically the same as adoption, lasts till child is 18. And is much easier to achieve. You are her grandmother anyway, so why does adoption matter that much to you.
You do not need parental consent for an adoption. But you do need a solicitor. Your child is old enough to state her own views on your adoption, and if birth mother hadnt been in contact for six years, that will all count when going for an adoption order. Also I am pretty sure you can adopt a child up to the age of 19.