To date, the Court of Appeal has seen it fit to block every subsequent application for permission to appeal Payne v Payne. This is presumably because of the rationale - as relied upon in Re D - that the delay inherent in progressing to the Supreme Court, followed by the additional delay of a re-trial, is deemed to be contrary to the best long interests of the children.
However, given the serious concerns Wall LJ expressed regarding the justness and thus the applicability of Payne, one may rightly suppose that a child's genuine long term interests would be best assessed by adopting fresh, child-centric criteria - as arrived at following a review by the Supreme Court - which would take into full account contemporary scientific research and evidence and the societal changes which have undoubtedly taken place since the time of Poel v Poel vis-a-vis the importance of a father in the life of his child.

Mr BD
The litigant-in-person father in Re D.