Stephen Lark has kindly sent me this interesting link about Waltheof. Among other things it gives six generations of descent from him and it's clear how he linked to Anne Neville by at least one route.
One area of Anne's ancestry that the coat of arms ignore is that of her descent from the House of York. This gave her some quite remarkable ancestors, including El Cid! I suppose it's proof that even the most complex of quarterings cannot convey everything.