The BBC released statements about their support for Android with iPlayer back in June: BBC iPlayer on mobile: a new version and Adobe Flash 10.1 streaming on all Android 2.2 phones and BBC iPlayer on Android update. This all boils down to saying that their current strategy for mobiles is to offer a mobile optimised version of their Flash site, and not to create individual apps for every smartphone out there.
I'm also a Flash-less fan of BBC Radio and TV (though in a better position than you as my manufacturer and carrier have announced that 2.2 is coming very soon), I had Beebplayer on my previous Android phone and it is sorely missed now.
For the moment I just subscribe to the podcasts of the shows I'm interested in (and luckily most of mine are available as podcasts) using the Google Listen podcast app, this does have the benefit that they work without cutting out while I'm on the tube!
EDIT: Going through the comments on some more recent articles on the BBC Internet blog I've discovered an app called Myplayer it seems to offer access to (as far as I can tell) the full iPlayer TV and radio library with both streaming and downloads for later viewing/listening. Picture quality doesn't seem quite as good as I remember from Beebplayer, so presumably its using a different stream. Anyway it's there and seems to work, grab it before "Aunty" spots it!
Newer EDIT: The BBC have released an official iPlayer app, called BBC iPlayer though this is really just a Flash wrapper around the mobile version of the website and does require a wifi connection before it will play most content.