Its not an issue that I'd lose sleep over.
Whether it ends up in landfill at all is of more concern, but once it does, it will degrade eventually, and how much difference the bag makes will vary (sometimes it will make a big difference). Of course if the bag is degradeable, this will help. Avoiding landfill is of more concern I'd say. Sorry for stating the obvious.
Meanwhile, the UK might actually be catching up on the US, Canada, much of Europe......... and various other countries on such issues:
"Recycling firm dreams of nappy days"
BBC NEWS | Business | Recycling firm dreams of nappy days
Meanwhile, would someone mind listing the options for parents, as I'm vaguely aware that there are quite a few, not just disposeable/washeable.